Brown Butter Dulce de Leche Cookie Cups

Preheat the oven to 350°F. Spray two 24 mini-muffin tins with nonstick cooking spray.
In a medium bowl, combine the flours, baking powder, baking soda, and salt. Set aside.
In a stainless steel sauté pan set over medium heat, melt the butter. Swirling the pan occasionally, continue to cook the butter. It should become foamy with audible cracking and popping noises. Once the crackling stops, continue to swirl the pan until the butter develops a nutty aroma and brown bits start to form at the bottom. Once the bits are amber in color, about 2 to 3 minutes after the popping stops, remove from heat and pour into a mixing bowl, scraping in all the browned bits.*
While the butter is still hot, stir in the granulated sugar and brown sugar. Let cool to just warm before adding in the vanilla, eggs, and yolk, one at a time, stirring well with a rubber spatula after each addition. Add the dry ingredients and mix until just combined.
Press a 1-tablespoon sized ball of dough into each mini muffin cavity. Bake for 12 to 15 minutes, or until edges are lightly golden brown and the center is set. Remove from oven and, using the round end of a wooden spoon or whisk, make 1-inch wide indentations into the center of each cookie.
While cookies are still warm, fill each cookie’s center with dulce de leche using a spoon or piping bag. Sprinkle with sea salt. Let cool completely before serving.