In a large bowl, cream together the butter, brown sugar, and granulated sugar with an electric mixer until combined and creamy, about 2 minutes. Beat in the egg and egg yolk until combined, followed by the vanilla extract. Lastly, beat in the baking soda, cornstarch, instant espresso powder and flour until a soft dough comes together. Fold in the chocolate chunks. Cover and chill in the fridge for at LEAST 2 hours. This is mandatory.
While dough chills, prepare your Nutella filling. Line a plate or small baking sheet with parchment. Spoon the Nutella into a zip-top bag and seal out the air. Snip off a corner and pipe little Hershey Kisses-size drops of Nutella onto the baking sheet. You should get about 16 drops. Freeze until firm.
Preheat oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicone liners. Using a Tablespoon or 2-Tablespoon-size cookie dough scoop, scoop out a mound of dough. Use your thumb to make an indentation in the center of the dough ball and push a Nutella drop inside. Cover the Nutella drop with the dough and place on the cookie sheets about 2" apart.
Bake for approx. 10-12 minutes, rotating pans halfway through cooking time until the tops look just about set. Do not over-bake, as these will continue to cook as they cool. Sprinkle the tops with coarse sea salt and allow to cool on the baking sheets.