Preheat the oven to 350°F/180°C (160°C for a fan oven), and line a baking sheet with parchment paper or a Silpat silicone baking mat. Set aside.
In a mixing bowl, with a hand mixer, cream the butter, powdered sugar, and vanilla extract until light and fluffy.
Add flour and salt, and beat at low speed until a smooth dough forms.
Use a small (1-inch) cookie scoop to drop the cookie dough onto the lined baking sheet, leaving about two inches between each cookie, and slightly flatten each ball of dough with your hand or a class glass.
Using a teaspoon measuring spoon, create a small indention in the center of each cookie.
Using a spoon or a piping bag, fill the indention with dulce de leche. Do not overfill.
Bake cookies for 11-12 minutes or until the bottoms are slightly browned. Allow to cool on the cookie sheet for 10 minutes, then transfer to a wire rack to cool completely.
Notes
Make uniform cookies: Use a cookie scoop or tablespoon to measure equal portions of dough for each cookie. This ensures that they all bake evenly and have a consistent appearance.
Don't overfill the thumbprints: Be careful not to overfill the thumbprint indentations with dulce de leche, as it may overflow and spread during baking. A piping bag or a small spoon can help you control the amount of filling used.
Presentation: Once the cookies are completely cooled, you can sprinkle them with powdered sugar or drizzle with melted chocolate for an extra touch of decadence.