Preheat oven to 375°F (190°C). Line a light- or medium-colored heavy-weight baking sheet with parchment paper or a silicone baking mat.
In a large bowl, beat 1 cup (2 sticks) unsalted butter (room temperature) and 2/3 cup granulated sugar with an electric mixer on medium-high speed for about 1 to 2 minutes, until light and fluffy. Scrape down the bowl as needed.
Add 1 large egg yolk and 1 teaspoon vanilla extract and beat just until combined.
Add 2 1/4 cups (280 g) all-purpose flour and 1/2 teaspoon kosher salt. Mix on low speed until the flour is incorporated and the dough comes together into a soft, cohesive ball. Do not overmix.
Roll the dough into 1-inch balls and place them on the prepared baking sheet about 2 inches apart.
Flatten each ball slightly with the ball of your hand. Use your thumb or the back of a small spoon to press a shallow indentation into the center of each cookie.
Bake for 8 to 10 minutes, or until the bottoms are just barely golden.
Remove the baking sheet from the oven. If any indentations have lost definition, gently re-press them with the back of a spoon. Fill each indentation with approximately 1/2 teaspoon dulce de leche (use the 6 ounces dulce de leche).
Return the baking sheet to the oven and bake an additional 3 minutes, until the dulce de leche levels out and the bottoms of the cookies are lightly golden.
Transfer the cookies to a wire rack and cool completely before serving.