Line an 8x8 baking dish with parchment paper. Add the 3 tablespoons of butter to a 10-inch skillet over medium heat and melt the butter. Add the 1⅔ cups chopped pecans to the butter. Stir continuously for 1-1½ minutes until the pecan pieces are completely coated and release a warm, nutty aroma. Transfer the toasted pecans to the lined baking dish.

You will need a medium-sized heatproof bowl to pour the browned butter into. Add the 1 cup of butter to a light-colored skillet over medium-high heat, stirring often. (I do not recommend using a nonstick or dark-colored skillet, you will need to be able to see the change in color to avoid burning the butter) Once the butter begins to foam and the milk solids are separating, the solids at the bottom of the pan will turn a golden brown and will smell nutty. Remove the skillet from the heat and pour it into a heatproof bowl. Do not leave the browned butter in the skillet, it will continue to cook and will burn. Allow the butter to cool completely.

Add the flour, cornstarch, baking powder, and baking soda to a medium-sized bowl. Whisk to combine. Set it aside.

Using a stand mixer or a large mixing bowl and a handheld mixer on medium-high speed, beat together the completely cooled brown butter, dark brown sugar, granulated sugar, and pure vanilla extract for 2-3 minutes until completely incorporated.

Lower the mixer speed to medium-low. Add the eggs one at a time, beating well after each egg.

Add 0.5 of the flour mixture at a time, mixing just until incorporated.

Add in the toasted pecan pieces and mix just until well combined. Cover and chill in the refrigerator for 3 hours. (You can chill the dough overnight)

Preheat the oven to 375°F. Line 2 baking sheets with parchment paper and set aside.

Depending on which size cookie you want, use either a 1.5 tablespoons or 1 tablespoon cookie scoop to scoop the cookie dough. Roll the dough into a ball. If you want to add sparkle, roll the dough ball in the coarse sanding sugar. Place the dough balls 2 inches apart on the prepared baking sheet. Gently press a pecan half onto the center of the dough ball. If you choose the 1.5-tablespoon scoop, bake for 9-10 minutes. If you choose the 1 tablespoon scoop, bake for 7-8 minutes. The cookie edges should look light golden brown. Allow the cookies to rest on the baking sheet for 2-3 minutes before transferring them to a cooling rack to cool completely.

For the caramel drizzle, add the caramel bits to a small microwave-safe bowl. Add 1.5 tablespoons of water to the caramel bits. Heat in the microwave for 30-second intervals, stirring well after each interval until the caramel is smooth. Drizzle the melted caramel over the tops of the cooled cookies. Allow the drizzle to harden before serving.