Begin by toasting the pecans. In a skillet over medium heat, melt 2 tablespoons of the butter. Add the chopped pecans and toast them, stirring occasionally, until fragrant and lightly browned, which should take about 5 to 8 minutes. Once toasted, transfer the pecans to a small bowl and set them aside to cool.

Using the same skillet, melt the remaining ½ cup of butter over medium-high heat. Let the butter cook until it begins to foam and turn golden brown, roughly 6 to 8 minutes. Keep a close eye on it to avoid burning. Once the butter is browned, quickly pour it into a large mixing bowl and allow it to cool slightly before proceeding.

Next, whisk the light brown sugar and granulated sugar into the browned butter, blending until smooth. Beat in the egg and vanilla extract, mixing thoroughly for about a minute, ensuring the ingredients are well incorporated.

In a separate medium-sized bowl, combine the all-purpose flour, baking soda, cornstarch, and salt. Gently fold the dry ingredients into the butter mixture, stirring just until no streaks of flour remain visible. Stir in the cooled, buttered pecans, ensuring they are evenly distributed throughout the dough. Cover the dough and refrigerate it for about an hour, or until it has firmed up.

While the dough chills, preheat your oven to 350°F (175°C). Line a couple of baking sheets with parchment paper.

Once the dough is ready, scoop out 1½ tablespoon-sized portions and roll them into smooth balls using your hands. For an extra touch, you can roll the dough balls in granulated sugar and press a pecan half into the top of each ball. Place the dough balls onto the prepared baking sheets, leaving about 2 inches of space between them.

Bake the cookies for 8 to 10 minutes, or until the tops appear dry and the edges are golden. Allow them to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.