Line a large baking sheet with parchment paper and set aside.

In the bowl of a stand mixer (or large mixing bowl), whisk together the flour, sugar, instant yeast, and salt. Add the eggs and vanilla, then pour in the warm milk and melted butter. Mix on low speed until the dough comes together, then knead for about 8–10 minutes until it feels smooth, elastic, and slightly sticky.

Shape the dough into a ball, place it in a lightly greased bowl, and cover with plastic wrap. Let it rest at room temperature for about 45 minutes, or until it doubles in size.

Lightly flour your work surface and roll the dough to just under ½ inch thick. Use a round cookie cutter to cut out donuts, re-rolling scraps as needed. Transfer the rounds to the prepared baking sheet. Cover loosely with plastic wrap and let them rise again for 45 minutes, until puffy.

Preheat your oven to 200°C (400°F) with the rack in the center. Bake the donuts for 12–15 minutes, or until the tops turn golden brown.

Allow the donuts to cool slightly. Using a sharp knife, cut a deep slit into the side of each donut. Fill a pastry bag fitted with a round tip with Nutella and pipe generously into the center of each donut.

Brush each donut with melted butter, then roll in sugar until lightly coated. Serve warm for the ultimate treat.