Cut the cold unsalted butter into small cubes.
In a large bowl or a stand mixer fitted with the paddle attachment, beat the cubed butter with the brown sugar and granulated sugar until creamy and smooth, scraping the bowl as needed.
Add the eggs and vanilla and mix until combined.
Stir in the cornstarch, baking powder, baking soda, and salt until combined.
Add the all-purpose flour and mix just until the dough comes together, then fold in the mini and regular chocolate chips.
Cover the dough tightly and chill in the refrigerator while you prepare the Nutella filling.
Line a sheet pan with parchment paper. Place a large scoop of Nutella into a small resealable plastic bag, seal, and snip off the tip; pipe approximately 1 teaspoon dollops of Nutella onto the prepared pan, spacing them apart, and freeze until solid, about 20 minutes.
Preheat the oven to 375°F (190°C) and line a dark-colored sheet pan with a silicone liner or parchment.
Portion the chilled dough into about 40-gram portions (roughly 2 packed tablespoons) or as desired; flatten each portion into two discs.
Place one frozen Nutella dollop onto a dough disc, top with the second disc, pinch edges to seal completely, then roll gently into a ball. Arrange balls on the sheet pan at least 2 inches apart; work in batches and freeze each pan of assembled cookies for 10 minutes before baking.
Bake straight from the freezer for 9–14 minutes, or until the tops no longer look gooey; slightly under-baked is preferred for a soft center.
Remove from oven and immediately sprinkle with fine sea salt if using, and optionally press a few extra chocolate chips into the tops. Cool on the sheet pan for 5 minutes, then transfer to a wire rack to finish cooling.