Line a small plate or baking sheet with parchment paper. Scoop 10 rounded teaspoons of Nutella onto the parchment. Freeze for at least 30–45 minutes, or until firm enough to handle.
In a large bowl, beat the softened butter, brown sugar, and granulated sugar until creamy, about 2 minutes. Add the egg, egg yolk, and vanilla. Mix until smooth and fully combined.
In a separate bowl, whisk together the flour, cocoa powder, cornstarch, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients and mix just until combined.
Fold in the chocolate chips or chopped chocolate. The dough should be soft and thick but not dry or crumbly.
Cover the cookie dough and refrigerate for 20–30 minutes. We don't want it rock-hard. We just need it firm enough to wrap around the Nutella.
Scoop about 3 tablespoons of cookie dough and flatten it into a thick disc. Place one frozen Nutella dollop in the center.
Bring the dough up and around the Nutella, completely sealing the filling inside. Roll gently into a tall ball.
Place the cookies several inches apart on a parchment-lined baking sheet. Press a few additional chocolate chunks into the tops.
Bake at 350°F for 10–12 minutes. The edges should look set, but the centers should still look soft and slightly underbaked. Don't wait until the centers look completely done.
Let the cookies cool on the baking sheet for 10 minutes. Sprinkle with flaky sea salt while they're still warm. Serve slightly warm for the gooiest Nutella center.