Preheat your oven to 350°F. Grease a 12-cup muffin pan and lightly flour a clean work surface.

Roll the pie crust into a 12-inch circle. Use a 3-inch cookie cutter to cut out 12 rounds. Gently press each round into a muffin cup so the dough rises slightly up the sides. Refrigerate the dough while making the filling.

In a bowl, whisk together light corn syrup, brown sugar, salt, melted butter, beaten egg, and vanilla extract until smooth. Stir in the chopped pecans.

Fill each dough-lined muffin cup with about 1 tablespoon of the pecan filling. Bake at 350°F for 25 minutes, or until the filling is set.

Allow the mini pies to cool in the pan for 10 minutes before transferring them to a wire rack to cool completely. If desired, pipe or scoop a small dollop of whipped cream on top of each mini pie.