Line a baking pan with parchment paper or silicone mat. Spoon about 2 teaspoons of Nutella dollops. Make the Nutella as round as possible using 2 small spoons and drop them onto the prepared pan. Freeze while you are preparing the cookie dough.
Cookie Dough
Cook butter in a medium saucepan over medium heat, stirring often until it foams, then browns for about 5–8 minutes. After it has browned, turn off the heat and remove the butter into a separate bowl. Let it cool completely before using.
Preheat oven to 375F/190°C. Line two large baking pans with parchment paper or silicone baking mats.
In a large bowl, combine together all-purpose flour, cornstarch, baking soda, baking powder, and salt. Set aside.
In a separate large bowl, whisk together cooled brown butter, brown sugar, and granulated sugar until well combined. Whisk in eggs and vanilla extract until well combined.
Add dry ingredients to wet ingredients and mix until well incorporated with a spatula. Then, fold in two-thirds of the chocolate chunks into the dough.
Assemble
Remove the Nutella from the freezer. Scoop 2 tablespoons of dough, flatten and put a Nutella ball on the middle. Gather the edges of the dough to cover the Nutella. Make sure the Nutella is fully covered to prevent leaking. Drop the dough onto the prepared baking pans and sprinkle the top with the remaining chocolate chunks.
Bake for 12-13 minutes, or until the edges are nicely browned. Cool for 5 minutes on the pan before removing to wire racks to cool completely.