Using a 1 teaspoon measure, scoop out Nutella and place in small drops on a cookie sheet lined with parchment. Place in the freezer for 15 minutes.
Preheat the oven to 350 degrees. Line 2 large baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking powder, and salt.
In the bowl of your stand mixer, beat together the butter and 1 1/2 cups granulated sugar on medium until light and fluffy, 3 to 5 minutes. Beat in the eggs, one at a time, and add in the the vanilla.
Turn the mixer to low and gradually beat in the flour mixture until just combined. Scrape down the bowl to ensure everything is well incorporated.
Place 1/3 cup granulated sugar in a small bowl. Use 2 tablespoons cookie dough for each cookie. Split the piece of dough in half and slightly flatten the bottom half by pressing it together with the palms of your hands.
Use a small metal spatula to lift the mounds of Nutella from the baking sheet and lay on the bottom half of cookie dough. If the Nutella starts to soften, place it back in the freezer for a few minutes.
Cover the Nutella with the other piece of cookie dough. Seal the edges with your fingers and roll the ball in the sugar to coat it. Place the cookies on the prepared baking sheet.
Repeat with the remaining dough and Nutella mounds, spacing the cookies about 2 inches apart from each other on the baking sheets.
Bake the cookies, one sheet a time, rotating from front to back halfway through baking. The edges will start to turn brown when they are finished, about 10 to 13 minutes. The centers should still be soft and puffy.
Remove the cookies from the oven and cool on the baking sheet for 10 minutes. Using a spatula, remove the cookies from the baking sheet and cool on a rack. They can also be served warm. Don't forget the milk!