Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. In a large bowl, cream together the softened butter and brown sugar until light and fluffy. Add the egg yolk and vanilla extract, and mix until well combined.

Gradually add the flour to the butter mixture, stirring until a soft dough forms. Shape the dough into 1-inch balls and place them on the prepared baking sheet, about 2 inches apart. Using your thumb or the back of a spoon, gently press down in the center of each ball to create a small indent for the filling.

In a small saucepan, combine the brown sugar, heavy cream, and butter over medium heat. Stir continuously until the sugar is dissolved and the mixture is smooth and slightly thickened, about 2-3 minutes. Remove from heat and stir in the vanilla extract and chopped pecans.

Spoon about 1 teaspoon of the pecan filling into the indent of each cookie. Be careful not to overfill, as the filling will spread slightly during baking.

Bake the cookies for 10-12 minutes, or until the edges are lightly golden and the filling is set. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.