Preheat the oven to 350°F.
Lightly sprinkle flour over a clean surface, then roll out the pie crust. Cut out 15 circles about 3 inches wide using a round cutter.
Place liners in each muffin tin cup. Gently press a dough circle into each lined cup to form a shell. Refrigerate the tin.
In a bowl, whisk together melted butter, brown sugar, egg, corn syrup, and vanilla extract until smooth.
Stir in the chopped pecans.
Remove the muffin tin from the fridge and spoon the pecan mixture into each crust.
Bake for 20 to 25 minutes, or until the pecan filling is set and the crust is golden brown.
Let the pies cool in the pan for about 10 minutes, then transfer them to a wire rack to cool completely.