Cut in cold butter until mixture resembles coarse crumbs.
Stir in pecans.
Roll dough into 1-inch balls and place on ungreased baking sheet.
Bake for 10-12 minutes, or until edges are lightly golden.
Meanwhile, prepare the pecan pie filling: In a saucepan, combine corn syrup, brown sugar, and egg. Cook over medium heat, stirring constantly, until mixture thickens slightly.
Stir in vanilla extract.
Remove cookies from oven and immediately press a thumb into the center of each cookie to create an indentation.
Spoon pecan pie filling into the indentations.
Let cool completely before serving.
Notes
Store cookies in an airtight container at room temperature for up to 3 days.