In a large mixing bowl, beat together the butter and sugar with an electric mixer on medium speed for 3 minutes. Beat in the vanilla and egg yolk.
In a separate bowl, combine the flour and salt. Stir with a whisk. Gradually stir the flour into the butter and mix just until blended.
Shape the dough into a ball, cover, and chill for at least 1 hour.
Preheat the oven to 350ºF.
Shape the dough into 1 tablespoon size balls and place them 2 inches apart on a parchment-lined baking sheet. Using your thumb or the back of a teaspoon, press a slight indention in the center of each ball. Take care not to press too far down. If the edges crack while making the indention, simply pinch them back together to smooth them out. Otherwise, cracks are okay.
Fill the indents with 1/4 teaspoon dulce de leche. Bake for 10-12 minutes or until the bottom edges are lightly browned.
Cool the cookies on the pan for 5 minutes before transferring them to a wire rack to cool completely. Sprinkle the tops lightly with sea salt.