Preheat your oven to 350°F and line a baking sheet with parchment paper.
In a saucepan over medium heat, melt the butter, stirring occasionally until it begins to foam and develops golden-brown specks with a nutty aroma. Remove from heat and allow to cool slightly.
In a large mixing bowl, combine the browned butter, brown sugar, and granulated sugar. Mix until incorporated.
Add the eggs and vanilla extract, mixing until combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
Gradually incorporate the dry ingredients into the wet ingredients until a dough forms. **The dough will be slightly crumbly, and that's okay!** Use your hands to gently press and mold the dough together until it holds its shape.
Scoop portions of dough and roll them firmly between your palms to create balls. Place them on the prepared baking sheet, leaving approximately 2 inches between each cookie.
Using your thumb or the back of a rounded measuring spoon, gently press an indentation into the center of each cookie to create a well for the pecan pie filling.
Bake for approximately 12 minutes at 350°F, or until the edges are lightly golden.
Immediately after removing the cookies from the oven, gently press the centers again while they're still warm to reinforce the wells. Allow the cookies to cool on the baking sheet before transferring them to a cooling rack.