Prepare a baking sheet with parchment paper. With a spoon or cookie scoop, scoop out 15 tablespoon-sized balls of Nutella onto the baking sheet. Freeze the Nutella balls until you're ready to add them to the cookie dough. You'll leave them in the freezer until the cookie dough has been chilled and you're ready to bake the cookies.
With a hand mixer, cream the butter, brown sugar, and granulated sugar in a large mixing bowl on medium speed for about 2 minutes.
Add the egg, egg yolk, and vanilla extract to the bowl, mixing until just combined. Set bowl aside while you sift the dry ingredients together.
In a second medium-sized bowl, combine sifted flour, baking soda, salt, and cocoa powder. Gradually add the dry ingredients to the bowl of wet ingredients as you mix. Mix the dough until all the ingredients are combined, making sure to scrape the sides of the bowl with a rubber spatula.
Cover the cookie dough with plastic wrap and let it chill in the fridge for 20-30 minutes. Preheat oven to 350℉.
When you're ready to make the cookies, take the dough out of the fridge and Nutella balls out of the freezer. Scoop out 3-4 tablespoons of cookie dough, flatten the dough in your hand like a pancake, and add the Nutella ball. Wrap the Nutella completely with the cookie dough, rolling the dough into balls. Bake the cookies on a parchment paper-lined cookie sheet 4 cookies at a time for 12-14 minutes.