Step 1: Brown the butter
Place half of the butter in a medium skillet over medium heat. Allow it to melt and cook while swirling the pan occasionally. The butter will bubble and foam before turning golden with small brown bits at the bottom. Once it reaches a medium caramel color and releases a nutty aroma, remove from heat and transfer to a heatproof bowl. Let it cool for about 20 minutes.

Step 2: Prepare the pecan meal
Add half a cup of pecans and the granulated sugar to a food processor. Pulse until the mixture becomes a medium coarse powder. Measure half a cup of this pecan meal and place it in a mixing bowl. Discard any extra.

Step 3: Combine dry ingredients
Add flour, cornstarch, salt, and baking powder to the pecan meal. Whisk everything together until evenly combined.

Step 4: Cream the butter and sugar
In a stand mixer, beat the remaining butter on medium speed for about two minutes until smooth and creamy. Add the brown sugar and continue beating for about four minutes until light and fluffy.

Step 5: Add brown butter
Pour in the cooled brown butter and mix for another one to two minutes until the mixture is smooth and well blended.

Step 6: Add egg yolk and vanilla
Reduce the mixer speed to low and mix in the egg yolk and vanilla extract.

Step 7: Add dry ingredients
Turn off the mixer and add the flour mixture. Mix on low speed until everything just comes together. Refrigerate the dough for 20 minutes.

Step 8: Shape the dough
Divide the dough into two portions. Place each portion on parchment paper and roll into logs about 10 inches long and 1 1/2 inches thick.

Step 9: Chill the dough
Refrigerate the dough logs for at least three hours or overnight until firm. For faster chilling, freeze them for about one hour.

Step 10: Slice and bake
Preheat the oven to 325°F. Slice the dough into quarter inch thick rounds and place them on a parchment lined baking sheet about one inch apart. Press a pecan half on top of each cookie and sprinkle with turbinado sugar if desired.

Bake for 13 to 15 minutes, rotating the pan halfway through baking, until the cookies are lightly golden and slightly puffed.

Step 11: Cool the cookies
Allow cookies to cool on the baking sheet for 15 minutes before transferring them to a wire rack to cool completely.