Preheat the oven to 350°F. Prepare a 9"x13" (22cmx30cm) pan by greasing it and lining it with parchment paper.
In a food processor, grind the pecans until they are fine, but not starting to stick together into a butter.
In the bowl of a mixer (or by hand) whip butter and honey until light and creamy. Beat in eggs, one at a time, until well incorporated, then add applesauce. The mixture will look curdly - that's okay.
Add the buckwheat flour, arrowroot or cornstarch, baking powder, ground chia seeds, cinnamon and ground pecans. Mix well.
Stir in the grated apple.
Spread the batter into the prepared pan.
Clean the bowl with a rubber spatula, but don't bother washing it because you can now make the topping in it. Mix all the ingredients for the crumble topping in the empty mixing bowl until crumbly. Spread the crumbles evenly over the batter in the pan.
Bake for 45 minutes, or until a toothpick inserted in the middle comes out clean.
Let cool slightly in pan, then cut into squares.
Serve with a dollop of whip cream or ice cream.
Keeps well at room temperature for several days.