Preheat oven to 350°F. Spray mini muffin tins with cooking spray or grease well with butter.
For the cookie base: Beat 1/2 cup butter and 1/2 cup brown sugar until fluffy. Mix in egg yolk and vanilla until combined.
Add flour and 1/4 teaspoon salt, mixing just until dough comes together. It will be slightly crumbly but should hold together when pressed.
Roll dough into 1-inch balls and press into the bottom and up the sides of each mini muffin cup, creating a small well in the center.
For the topping: Whisk together melted butter, 1/2 cup brown sugar, corn syrup, egg, vanilla, and 1/8 teaspoon salt until smooth.
Stir in the toasted chopped pecans until evenly coated with the mixture.
Spoon about 1 teaspoon of pecan filling into each cookie cup, filling almost to the top (they won't rise much).
Bake for 15-18 minutes until the filling is set and the edges are golden brown.
Cool in the pan for 10 minutes (this is important—they need time to set!), then carefully run a knife around the edges and transfer to a wire rack to cool completely.