Prepare your Nutella filling first by lining a cookie sheet with wax paper and dropping Nutella by 2 teaspoon-sized dollops onto cookie sheet. Place in freezer to harden while you prepare your cookie dough.
Cut your butter into Tablespoon-sized pieces and place in a medium-sized saucepan. Melt over medium-low heat.
Once butter has melted, increase heat to just above medium heat.
Swirl and scrape the sides of the pan frequently with a wooden spoon or heatproof spatula - the butter will bubble and pop. Once the bubbling/popping slows, the butter will begin to turn brown, it will look like this once it's finished:
Watch the butter very carefully at this point, and once it begins to brown and you smell the nutty aroma of browned butter, remove from heat quickly and pour into a large, heatproof bowl.
Allow butter to cool for 25-30 minutes before proceeding with the recipe.
For the Cookie Dough
Preheat oven to 375F (190C) and line cookie sheets with parchment paper. Set aside.
Add sugars into cooled browned butter, stir well.
Stir in eggs, one at a time, stirring well after each addition.
Add vanilla extract and stir.
In a separate, medium-sized bowl, whisk together flour, cornstarch, baking powder, baking soda and salt.
Gradually add flour mixture to butter mixture, stirring until ingredients are completely combined.
Add your finely chopped chocolate bar and stir well.
Chill dough in refrigerator for 15-20 minutes.
Remove frozen Nutella from freezer and cookie dough from refrigerator (if at any point the Nutella becomes too sticky and hard to work with, return to freezer for at least 5-10 minutes)
Scoop dough by heaping 1 ½ Tbsp-sized spoonful and press frozen Nutella dollop into the center. Form around Nutella until it is completely concealed (add more dough as needed).
Roll into an even ball and place on a wax-paper lined sheet. Repeat until all Nutella dollops are concealed in cookie dough, and freeze cookie dough balls for 15 minutes.
Place cookie dough at least 2 inches apart on parchment paper-lined sheet, and bake on 375F (190C) for 12-13 minutes, or until edges are just beginning to turn golden brown.
Sprinkle immediately with sea salt. Allow cookies to cool completely on cookie sheet before removing (they'll be quite fragile when warm, but will become more sturdy as they cool).