Prepare the dough. Preheat the oven to 350°F (175°C). Have an 11 × 16-inch jelly roll pan or a 9 × 13-inch baking pan ready.
Using a hand mixer or stand mixer, beat the softened butter with 1/2 cup sugar until the mixture becomes pale, light, and fluffy.
Mix in the egg yolk and salt until thoroughly incorporated.
Add the flour gradually, continuing to mix until a crumbly dough forms.
Press the dough evenly across the bottom of the prepared pan. Lightly flour your hands as needed to keep the dough from sticking while pressing it into place.
Prepare the meringue. Using a mixer fitted with a whisk attachment, whip the egg whites until stiff peaks develop.
Slowly incorporate 1 cup sugar while continuing to beat the whites. Whip until the meringue is firm and glossy.
Carefully fold the finely ground walnuts and lemon extract into the meringue without excessively stirring or deflating the whipped whites.
Assemble the layers. Stir or loosen the blackberry jam with a fork until it is easy to spread, then distribute it evenly over the unbaked dough.
Gently spread the walnut meringue across the jam layer, creating light swirls over the surface if desired.
Scatter the chopped walnuts evenly over the meringue.
Bake the cookies. Transfer the pan to the preheated oven and bake for approximately 40 minutes, or until the meringue develops a crisp, golden surface.
Watch the cookies toward the end of baking so the meringue does not become excessively browned.
Cut and cool. Remove the pan from the oven and cut the cookies into pieces while they are still warm. Use a serrated knife with a gentle back-and-forth sawing motion to minimize cracking or crushing the fragile meringue.
If a section of meringue breaks away during slicing, carefully press it back against the jam layer beneath it.
Allow the cookies to cool completely, either in the baking pan or after transferring them to a wire cooling rack.