TO MAKE THE COOKIES: Preheat oven to 350F (180C). Line two cookie sheets with parchment, or spray with nonstick spray.
In a glass measuring cup or small bowl, whisk together the agave, chia seeds, soymilk, vanilla and lemon extraact. Set aside while you measure the dry ingredients, or at least 2 minutes.
In a large bowl, sift together the flour, xanthan gum, baking powder and salt. Whisk to combine evenly. Drop the coconut oil in large chunks over the flour mixture. Then, using your hands, pinch the mixture between your thumb and forefingers repeatedly until it comes together and the oil is completely blended into the flour. The mixture should appear crumbly but hold together when squeezed in your hand. (Note: the dough should NOT be the same as a pie dough, with visible, pea-sized bits of coconut oil distributed throughout; it should all be smoothly and completely blended into the flour).
Pour the wet mixture over the dry and stir well to combine. You should have a soft and sticky dough, but one that holds together.
Gather the dough and form into a disk. Wrap in plastic wrap and refrigerate until firm, about an hour. Once firm, remove the dough from the plastic and place on a lightly floured piece of waxed paper or countertop and roll out to about 1/4 inch (.5 cm) thickness. Cut into rectangles about 3 x 2 inches (8 x 5.5 cm) big. Place the cookies about 1 inch (2.5 cm) apart on cookie sheets. Gather any remaining dough and roll again; repeat until all dough is used.
Bake in preheated oven for 10-13 minutes, rotating the cookie sheets about halfway through, until cookies are deep golden brown on the edges. Cool completely before removing from the cookie sheets. Makes 24-30 cookies. May be frozen: wrap in plastic and store in an airtight bag or container in the freezer until ready to use, up to 3 months
TO MAKE THE "WHITE CHOCOLATE" COATING:Place all ingredients in a high-powered blender (I use a VitaMix) and blend until perfectly smooth and almost liquid; this will take some time, and you will have to push the mixture toward the blades using the tamper. When it's done, it should be pourable and the consistency of a very thin natural almond butter. Use immediately to make the Cookie Crumb Garnish.
TO MAKE THE COOKIE CRUMB GARNISH: Have the freshly made "White Chocolate Coating" at the ready.
Break the cooled cookies into chunks and place them in a food processor. Process until you have coarse crumbs. No pieces should be larger than a pea. Turn the crumbs into a medium bowl.
Pour the fresh white chocolate coating over the crumbs in the bowl. Toss with a fork until they begin to clump together and form little balls; keep tossing until all the crumbs are coated. If the mixture seems too wet, place the bowl in the refrigerator for 10 minutes and then toss again; repeat until the coating is firm and you have a bowl of little clumps. Break apart with your fingers if necessary to ensure that none of the pieces is larger than a pea. If you're making the garnish ahead of time, transfer to a covered container and store in the refrigerator. Otherwise, refrigerate until ready to use.
Strawberry Spread and Final Assembly
Separate 2 heaping cups of berries (about 15 large berries), choosing the most beautiful looking ones for this purpose. If you're making the cake now, hull and slice about 2/3 of the berries into slices; hull and quarter the other third of the berries (keep the two piles separate). The slices will be used beween the cake layers and the quartered berries will be used as garnish on top. If you're making the cake a day or two later, don't slice or cut the separated 2 cups (480 ml) of berries; leave those whole, and store them in the fridge until you need them. Slice and quarter right before you assemble the cake.
Hull the remaining berries (everything but the 2 cups you removed) and wash well. Place berries in a blender, in batches if necessary, and purée until liquefied. Transfer the liquid to a medium pot. Squeeze in the lime juice and stir.
Bring the mixture to a boil over medium heat, then lower heat to medium-low and cook, stirring frequently to avoid scorching, until the mixture reduces to 2-1/2 cups (600 ml) total (about half the original volume), 1-1.5 hours. Add the stevia and adjust sweetness level if necessary. Whisk in the agar and simmer for another 10 minutes, stirring constantly. Remove from heat and transfer the mixture to a bowl. Allow to cool until it reaches room temperature, then transfer to the refrigerator and refrigerate until cold (it will be firm at that point). If making ahead, store, covered, in the refrigerator up to 2 days (and keep your fresh berries in the refrigerator as well until ready to use).
TO ASSEMBLE THE CAKE: Keep the cake layers frozen (they will defrost very quickly--mine were defrosted by the time I assembled and finished photographing the cake--but it's much easier to assemble everything with frozen layers). Bring all your other components to your work station: the coated cookie crumbs, the pastry cream, the strawberry spread and the sliced and quartered fresh berries.
Measure out one cup (240 ml) of the cookie crumbs and set aside for garnish. Divide the remaining cookie crumbs in half.
Place one frozen cake layer on the center of a cake platter or serving plate. Cover the top with half the pastry cream; spread evenly with an offset spatula or the back of a spoon. Sprinkle with one half of the (non-garnish) cookie crumbs. Measure out 2/3 cup (160 ml) of the strawberry spread and dot the top of the cake layer with spoonfuls of it evenly over the crumbs, then spread it as evenly as possible to cover the surface evenly using the back of a spoon. Sprinkle with half the sliced fresh berries.
Top the first layer with another frozen layer, and repeat the toppings, first spreading with the rest of the pastry cream, sprinkling with the other half of the non-garnish cookie crumbs, covering with 2/3 cup (80 ml) of the strawberry spread, and sprinkling with the other half of the sliced berries.
Place the final frozen layer on top of the cake. Cover the top with 2/3 cup (160 ml) of the strawberry spread, leaving about 1/4 inch (1 ml) of cake uncovered around the edge. Sprinkle with the quartered strawberries and the cookie crumbs you reserved for garnish. (You may have a bit of the strawberry spread left over at this point; if so, store in a jar in the fridge up to 4 days. It's great as a jam or atop pancakes).
At this point, you may serve the cake immediately, or store, covered, in the refrigerator for 6-24 hours. Serve cold, from the fridge. Makes 8-10 stupendous servings. It doesn't keep well, so should be made for an occasion with 8-10 eaters, if possible. . . the cake will absorb moisture from the spread and will seem more like a trifle by day two (not that there's anything wrong with that. . . . ).