Heat the oven to 350°F. Line a baking sheet with parchment paper.
In a bowl, whisk butter and brown sugar until smooth and creamy.
Stir in milk and vanilla extract until combined.
Add flour, baking powder, and salt. Mix until a soft dough forms.
Roll dough into balls, about 1 tablespoon each. Place them on the baking sheet.
Press a small well into the center of each ball using your thumb or spoon.
In another bowl, stir chopped pecans, corn syrup, brown sugar, melted butter, and vanilla extract.
Spoon pecan filling into each cookie well.
Bake for 12–14 minutes until the edges look set and the centers look glossy.
Let cookies cool on the pan for 5 minutes, then move to a rack.