Check that an oven rack is in the middle position and preheat oven to 350°F. Butter a 9x13 glass baking pan and set aside.

In a medium sized saucepan, melt 3/4 cups butter on medium heat (approximately 5 minutes). When the butter begins to foam, continuously stir until the melted butter looks clear and there are lightly browned solids in the butter (7-10 minutes). Immediately remove from heat and set aside to cool.

In a medium sized mixing bowl, combine 2 cups flour, 1/4 cup sugar, and salt with a spatula. Zest one lemon over the bowl, mix. Add the browned butter (including the browned bits) and vanilla extract and mix. Scrape the shortbread mixture into the buttered 9x13 pan and use spatula to spread the shortbread mixture to the edges of the dish. Set aside the mixing bowl to make the lemon filling.

Use a metal tablespoon to press shortbread dough up the edges of the sides of the pan to create a 1/2 inch wall. Use the tines of a fork to poke some holes in the base of the shortbread dough. When the oven is hot, place the baking dish on the middle rack for 15-17 minutes until the is shortbread crust slightly golden in color.

While the crust is baking, make the lemon filling in the shortbread crust mixing bowl. Add 1 cup sugar, 1/4 cup flour, baking powder, and mix. Zest the remaining lemon over the bowl, mix with a spatula. Add the eggs and mix. Juice the two lemons, add the juice to the filling mixture, and mix until smooth. Set aside.

When the shortbread crust is ready, take the crust out of the oven and pour the filling over the hot crust. Carefully return the pan to the oven. Bake for 25-30 minutes. The lemon bars are ready when the edges look golden brown and the filling is not runny.

Place the baking dish on a wired cooling rack and allow the dessert to cool to room temperature (2 hours). Wrap and refrigerate until ready to serve. Cut the dessert into 24 pieces in a 4x6 grid. Use a sifter to sprinkle some powdered sugar (optional). Refrigerate any leftovers in an airtight container.