Heat the oven to 350°F (175°C) and line baking sheets with parchment paper. Beat the softened butter and granulated sugar until light and creamy, about 2 minutes.

Mix in the egg yolk and vanilla extract. Add the flour and salt, then mix just until a soft dough forms.

If the dough feels soft or sticky, cover and chill it for about 30 minutes. Scoop roughly 1 tablespoon of dough for each cookie and roll the portions into smooth balls.

Arrange the dough balls about 2 inches apart on the prepared baking sheets. Press a deep indentation into the center of each ball with your thumb or the rounded end of a small measuring spoon, repairing any cracks around the edges.

Combine the brown sugar, finely chopped pecans, melted butter, corn syrup, cream or milk, vanilla, and pinch of salt. Place about 1/2 teaspoon of filling into each indentation without overfilling.

Bake for 10–13 minutes, until the cookie edges are lightly golden and the filling is bubbling. Let the cookies rest on the baking sheet for about 5 minutes, then transfer them to a rack to cool for another 10–15 minutes.