• Place butter in a medium saucepan over medium heat. Once the butter is melted, swirl the pan occasionally to help promote even browning of the butter. Foam will form on top, this is normal!
• As the butter browns, it will bubble and sputter and the foam will begin to dissipate a bit. Keep a close watch on the butter, as it's easy to burn! It's easy to know when the butter is done: it will be quiet! Just listen for the bubbling and sputtering to be nearly stopped, then it's perfectly browned! The browning process typically takes 10-15 minutes total.
• After removing the browned butter from the heat, pour the browned butter into a heatproof bowl. Place the bowl in the refrigerator to help the butter solidify, stirring every 20 minutes or so. The stirring helps the butter to cool evenly and redistributes the browned milk solids throughout the butter. Your goal is to have a "softened butter" texture to use in the recipe. This took about an hour and a half for me.

For Cookies

• Line baking sheets with parchment (see note) and set aside.
• In a medium bowl, combine the flour and salt. Set aside.
• In the bowl of a stand mixer, combine the butter and sugar. Beat until light and fluffy, scraping down the sides of the bowl as needed.
• Add egg yolks, caramel extract (see note), and 2 Tablespoons dulce de leche. Mix to combine.
• Gradually add the flour/salt mixture and mix until you don't see any more flour. The mixture will be a crumbly and won't have formed a ball, and that's okay. Stopping the mixer when the ingredients are just combined will help keep the cookies tender.
• If using cookie stamps: Gently press the dough into a disc. I used a bowl scraper (see note) to help with this, to press the dough together while keeping my hands cleaner and working the dough less. (If making traditional thumbprints, move onto the next step.)
• If using cookie stamps: Roll the dough out to about ¼-inch thickness between two sheets of parchment paper. It may seem like a fool's errand in the beginning because the dough is crumbly, but I promise it will come together!

   

  If making traditional thumbprints: Portion the dough into 1-Tablespoon size balls (see note) and roll between your palms to make them round. Because the dough is a little crumbly, it may feel like it's not coming together right away. Just keep rolling and it will work! Roll the cookies in sugar, if desired.
• If using cookie stamps: Cut out shapes and place on prepared baking sheet at least an inch apart. Chill the dough 30 minutes before baking to help ensure the cookies keep their shape.

   

  If making traditional thumbprints: Place the cookies on the prepared baking sheets at least an inch apart. Using a fingertip or thumb, make an indentation in the center of each cookie. Chill the dough 30 minutes before baking to help ensure the cookies keep their shape.
• Once the cookies have chilled, preheat your oven to 375° F.

   

  Bake the cookies until just barely golden, 7-9 minutes for stamped cookies, or 5-7 minutes for traditional thumbprints. I got 36 stamped cookies/46 thumbprints with this recipe.
• Immediately upon pulling from the oven, use a small measuring spoon to press down the centers of the cookies if they rose at all during baking. Cool the cookies on the pan for 10 minutes, then remove to a wire rack to cool completely.
• Once cooled, fill each indentation with dulce de leche. I found that warming the dulce the leche made it easier to work with, and I used a small piping bag to pipe the caramel into the center of each cookie. Sprinkle each cookie with flaky sea salt, if desired. I used Vanilla Salt on mine (see note)!
• The cookies will keep in an airtight container on your counter for up to a week. The cookies can't be stacked unless you put parchment or wax paper between the layers.

   

  If you'd like to freeze the cookies, bake, cool, and then freeze unfilled. Then just thaw and fill.