Center a rack in the oven and preheat the oven to 350 (F). Prepare your cookie trays by lining with parchment paper or a Silpat mat.
Place 10 ounces finely chopped semisweet chocolate in a double boiler over medium heat (or, in a heatproof bowl over a saucepan of very hot water, with the bottom of the bowl NOT touching the water). Use a rubber spatula to stir the chocolate occasionally until it is melted and smooth. Once the chocolate is completely melted, remove heat and allow to cool for 5 to 10 minutes as you go through the other recipe steps.
In a medium bowl, whisk together 1/2 cup plus 2 tablespoons all-purpose flour, 1/2 tablespoon plus 1/2 teaspoon unsweetened cocoa powder, 1/4 teaspoon baking powder and 1/4 teaspoon kosher salt.
In the bowl of a freestanding electric mixer fitted with a paddle attachment, combine 5 tablespoons unsalted butter and 1 cup plus 2 tablespoons granulated sugar. Beat together on medium-high speed until well combined and the mixture has turned light and fluffy, around 5 minutes. Once the mixture is light and fluffy, slow the mixer to its lowest setting and add 3 eggs, one at a time, only adding the next egg until the previous egg before it has been fully incorporated into the batter. Once all the eggs have been added, scrape down the sides of the bowl with a rubber spatula. Increase the mixer speed to medium-high and beat for another 2 to 3 minutes until the mixture is very light, creamy, and pale in color.
Once the mixture is light and cream, lower the mixer to its lowest setting and add the slightly cooled melted chocolate (from the 2nd step) and 1/2 tablespoon vanilla extract and mix until just combined and the batter is a uniform chocolate color.
Remove the bowl from the mixer and sprinkle the dry ingredients (from the 3rd step) evenly over the surface of the chocolate mixture, before folding them in using a rubber spatula. BE CAREFUL NOT TO OVERWORK THE BATTER AFTER YOU ADD THE FLOUR, or your cookies will be tough and I will cry for you. Simply fold until the dry ingredients have just been incorporated — it's okay to have one or two flour streaks left.
Once the flour mixture has been incorporated, fold in 1 cup milk chocolate chips and stir until just evenly dispersed.
Once the chocolate chips have been folded in, drizzle some of the 1/2 cup of dulce de leche caramel on top of the batter — DO NOT MIX IN. Unmixed dulce de leche drizzle is what gives the cookies their interesting swirls. Use a 2-tablespoon sized cookie dough scoop to portion out the cookies as soon as you finish making the batter. The batter will be very soft at first, but it firms up quickly as it sits so act fast. Scoop each portion onto the parchment lined baking sheets, placing them about 2 inches apart. Continue drizzling dulce de leche over the batter before scooping until all the dulce de leche is used. Bake the cookies in the preheated oven until they are cracked all over the tops and softly set, about 14 to 16 minutes. Remove the pans from the oven and cool on a wire rack. Allow the cookies to cool completely before removing them from the baking sheets with a metal spatula.