Line a 9x13-inch pan with foil, leave a slight overhang along the edges. Lightly butter the entire foil-lined pan.
Prepare the crust: Have a medium heat-proof bowl on hand for the brown butter.
In a large saucepan, melt the butter over medium-low heat. Increase the heat to medium and, stirring occasionally, cook the butter until it turns golden brown and develops a nutty aroma. Depending on the stove's heat, it can take 5-8 minutes for the butter to brown properly. During this process the butter will first become foamy before changing color, making it difficult to see what's going on. Just be sure to give it a good stir now and then so that the butter doesn't burn. Once it's gorgeous and fragrant, remove the pan from the heat and transfer the butter to a heat-proof bowl. Cool till lukewarm. [Note: while the butter is cooling, give it a stir now and then, just to prevent it from solidifying. You just want to butter to be cool enough so that it won't scramble the eggs when they're added.]
In a large bowl, combine the cooled brown butter, 3/4 cup of sugar, and salt. Stir till well blended. Add the yolks and the almond extract, whisk until smooth. Using a large rubber spatula or wooden spoon, stir in the flour until you have a stiff dough. [It will have a very odd, dense texture for shortbread, but it will bake up beautifully, so don't worry.] Transfer about 2 cups of the dough to the foil-lined pan and press it evenly onto the bottom.
Refrigerate pan for about 40 minutes.
Topping: Add remaining 1/4 cup of sugar and hazelnuts to leftover dough, and using your fingertips, work the sugar & nuts into the dough until becomes crumbly; set aside.
Divide the oven, placing one rack second from the bottom, and the other second from the top. Heat the oven to 325 F.
Remove the pan from the refrigerator and prick the crust several times with a fork. [Chilling and pricking the dough will keep it from puffing up too much in the oven.] Place the pan on the lowest oven rack and bake the dough for about 15 minutes, just until the crust begins to set. Don't worry if the center still looks doughy, it's better to under-bake it at this stage.
While the crust is baking, begin preparing the filling;
In a large bowl, combine apples, jam, lemon zest, lemon juice, honey and sugar. Stir till well combined.
Spread filling over warm partially-baked crust. Scatter remaining topping mixture over filling.
Place pan on the highest of the 2 racks and increase the temperature to 350F. Bake for 20-25 minutes, or until the crumb topping is golden.
Remove pan from the oven and place on a cooling rack. Cool for at least an hour before removing the bars from the pan (use the foil overhang to lift them out of the pan).