Slice the unsalted butter into tablespoon-sized portions and transfer the pieces to a medium saucepan.
Melt the butter over medium-low heat. After it has completely liquefied, raise the heat to slightly above medium.
Frequently swirl the saucepan while scraping along the sides with a wooden spoon or heat-resistant spatula.
Continue cooking and stirring until the butter develops a golden-brown color and gives off a distinct nutty fragrance.
Immediately remove the saucepan from the heat and transfer the browned butter to a large heatproof mixing bowl. Leave it to cool for 25–30 minutes.
Preheat the oven to 375°F (190°C). Cover the cookie sheets with parchment paper.
Spoon the Nutella into 2-teaspoon portions on a cookie sheet lined with wax paper. Transfer the tray to the freezer and allow the portions to firm.
In a medium bowl, thoroughly whisk together the 2 3/4 cups plus 2 tablespoons all-purpose flour, cornstarch, baking powder, baking soda, and salt. Set this mixture aside.
When the browned butter has sufficiently cooled, add the brown sugar and granulated white sugar. Stir until the ingredients are evenly blended.
Incorporate the eggs individually, mixing thoroughly after adding each one.
Pour in the vanilla extract and continue stirring until it is completely distributed throughout the mixture.
Add the prepared dry ingredients gradually to the butter mixture, stirring until a cohesive cookie dough forms and no dry flour remains.
Finely chop the semisweet chocolate bar, then fold the chocolate pieces evenly into the dough.
Refrigerate the completed dough for 15–20 minutes so it becomes firmer and easier to shape.
Take the firm Nutella portions from the freezer and remove the chilled cookie dough from the refrigerator.
Scoop out heaping 1 1/2-tablespoon portions of dough. Press one frozen Nutella portion into the center of each piece.
Carefully bring the cookie dough around the filling until the Nutella is completely enclosed, then gently roll the dough into a uniform ball.
Continue the process until every Nutella portion has been fully wrapped in cookie dough.
Place the assembled dough balls in the freezer for 15 minutes so they remain firm enough to retain their shape during baking.
Arrange the chilled cookie dough balls on the parchment-lined baking sheets, leaving a minimum of 2 inches between each cookie.
Bake for 12–13 minutes, stopping when the outer edges are just beginning to become golden brown.
As soon as the cookies come out of the oven, lightly scatter sea salt over their tops.
Leave the cookies on the baking sheet until they have cooled completely before removing them.