In a skillet over medium heat, melt 2 tablespoons of butter. Add the chopped pecans and cook until toasted, 5 to 8 minutes, stirring occasionally. Transfer the buttered pecans to a small bowl and let cool.

In the same small skillet, heat the remaining ½ cup butter over medium-high heat. Cook until butter foams and browns, 6 to 8 minutes. Immediately transfer to a large mixing bowl and let cool for a few minutes.

Whisk the sugars into the browned butter. Whisk in the egg and vanilla until very well combined, about 1 minute.

In a medium mixing bowl, whisk together flour, baking soda, cornstarch, and salt. Fold the flour mixture into the butter mixture, mixing just until the last streaks of flour disappear. Stir in the buttered pecans until evenly dispersed. Cover and chill until dough is firm, about 1 hour.

Preheat oven to 350°F. Line baking sheets with parchment paper.

Scoop the chilled dough into 1½ tablespoon-sized balls and roll into smooth balls between your palms. If desired, you can roll the balls in extra granulated sugar and press a pecan half in the center. Place on the baking sheets 2 inches apart.

Bake for 8 to 10 minutes or until the tops appear dry and the edges are lightly golden brown. Let cool slightly on the pan, then transfer to a wire rack to cool completely.