Preheat the oven to 350°F (175°C) and lightly grease a 12-cup mini muffin tin.
In a mixing bowl, combine the flour and salt. Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs. Add ice water, 1 tablespoon at a time, until the dough just comes together.
Roll out the dough on a floured surface to about 1/8-inch thickness. Use a 3-inch round cutter to cut out circles, then press each into the muffin tin to form mini pie crusts.
In a separate bowl, whisk together the corn syrup, brown sugar, eggs, melted butter, and vanilla extract until smooth. Stir in the chopped pecans.
Spoon the filling evenly into the prepared crusts, filling each about 3/4 full. Bake in the preheated oven for 20-25 minutes or until the filling is set and the crusts are golden brown.
Remove from the oven and let cool in the tin for 10 minutes before transferring to a wire rack to cool completely.