In a mixing bowl, combine all-purpose flour, softened unsalted butter, granulated sugar, and salt. Blend until it resembles coarse crumbs. Stir in vanilla extract and egg yolk, then mix until dough forms. Wrap in plastic wrap and chill for 30 minutes.

Preheat oven to 350°F (175°C). Roll out chilled dough to about 1/8-inch thickness. Cut circles with a round cookie cutter that fit mini muffin tins. Press dough into each cup snugly.

Combine chopped pecans, light corn syrup, brown sugar, vanilla extract, salt, and beaten egg in a large bowl. Mix until well combined, ensuring pecans are evenly coated.

Spoon pecan filling into each prepared tart shell, filling about 3/4 full. Spread evenly with a small offset spatula or back of a spoon.

Bake in preheated oven for 20-25 minutes until edges are golden brown and filling is set. Monitor closely to prevent over-browning.

Remove from oven and let cool in pans for about 5 minutes. Transfer to a wire rack to cool completely before serving or storing.