Brown butter in a medium saucepan (be careful not to burn it). Remove from heat and pour into a heatproof storage container, cover with plastic wrap and freeze for 30 minutes, or until cool (alternately you can just let it rest at room temp or in the fridge until cool, it will just take longer).
In a mixing bowl, whisk together flour, cornstarch, cinnamon, baking powder, baking soda and salt for 30 seconds, set aside. Remove butter from freezer and pour into the bowl of an electric stand mixer (use a rubber spatula to scrape out any excess).
Add light-brown sugar, granulated sugar and vanilla to butter. Fit mixer with the paddle attachment and whip on medium-high speed until slightly pale and fluffy, about 4 minutes. Add in eggs one at a time, mixing after each addition until combined.
With mixer set on low speed, slowly add in dry ingredients and mix just until combined (if at this point your dough seems dry, stir in 1 Tbsp of milk). Stir in chocolate chips. Cover bowl tightly with plastic wrap and refrigerate for 30 minutes - 1 hour.
Preheat oven to 350 degrees. Remove cookie dough from refrigerator. Scoop dough out about 2 1/2 Tbsp at a time, flatten dough into a thin bowl shape and add a heaping tsp of dulce de leche to the center of dough.
Wrap dough around dulce de leche, being sure to fully enclose. Place on parchment paper lined baking sheet. Repeat with remaining dough and spacing cookies 2 1/2-inches apart.
Bake in preheated oven 10 - 12 minutes. Allow to cool several minutes on baking sheet then transfer to a wire rack to cool. Store in an airtight container at room temperature.