Preheat your oven to 350°F (175°C). Grease the muffin tin with a little butter or cooking spray to prevent sticking.

In a mixing bowl, combine the flour, powdered sugar, and salt. Add the softened butter and egg yolk. Mix until a dough forms and is smooth.

Roll out the dough on a lightly floured surface to about ⅛ inch thick. Use a round cutter or a glass to cut out circles that will fit into the muffin tin.

Press each circle of dough into the bottom and sides of the muffin tin cups. Prick the bottoms with a fork to prevent bubbling during baking.

Bake the tart shells in the preheated oven for about 15 minutes, or until lightly golden. Remove and let cool while preparing the filling.

In a saucepan over medium heat, combine the brown sugar, corn syrup, and heavy cream. Stir until the sugar dissolves completely and the mixture is bubbling. Allow to simmer for about 2-3 minutes.

Remove the saucepan from heat and stir in the vanilla extract. Allow the caramel to cool slightly before adding the chopped pecans.

Spoon the caramel-pecan mixture into each tart shell, filling them generously but not overflowing.

Bake the tarts for an additional 10-12 minutes until the filling is bubbly and slightly set. Remove from the oven and let cool.

Allow the tarts to cool to room temperature before carefully removing them from the muffin tin.