Begin by browning the butter. Place the butter in a light-colored frying pan over medium-low heat. As the butter melts, it will start to separate. Stir frequently. The cream-colored solids will begin to toast and eventually turn brown. Once the butter becomes mostly silent and the cream-colored bits have completely browned, remove the pan from the heat immediately and transfer the butter to a large bowl, scraping the pan to collect all the browned bits. Allow the brown butter to cool.

In the same bowl, add the sugars, salt, baking soda, baking powder, and vanilla extract. Use a whisk or hand mixer to blend everything together thoroughly. Next, incorporate the milk, egg, and egg yolk, and beat until the mixture is light and fluffy. Add the dry ingredients to the bowl, and if you were using a whisk, switch to a rubber spatula. Stir until the dry ingredients are fully combined. Gently fold in the chocolate chips. Cover the bowl with plastic wrap and set it aside on the counter for about 30 minutes.

To shape and bake the cookies, preheat your oven to 350°F (175°C) and line two greased baking sheets with parchment paper. Scoop about 2 tablespoons of dough per cookie. Create a well in the center of each dough ball and shape it into a small bowl. Use two spoons to fill the well with marshmallow fluff, ensuring it almost reaches the rim of the dough bowl. Gently press the sides to seal it slightly. Optionally, top the fluff with more chocolate chips or a small piece of chocolate. For cookies with 2 tablespoons of exposed dough, bake for about 12 minutes, or until the edges are golden brown.