Preheat your oven to 350°F (175°C). Generously grease a 6-cavity donut pan with nonstick spray or butter, making sure to coat every ridge and the center posts.
In a large mixing bowl, whisk together the flour, cocoa powder, sugar, baking powder, baking soda, and salt until no lumps remain and the mixture is evenly combined.
In a separate medium bowl, whisk the egg until lightly beaten. Add the milk, warmed Nutella, melted butter, and vanilla extract, whisking until smooth and fully incorporated.
Pour the wet ingredients into the dry ingredients. Gently fold together using a rubber spatula just until combined, about 15-20 strokes. The batter should be thick but pourable, with a few small lumps remaining.
Transfer the batter to a piping bag or large zip-top bag with one corner snipped off. Pipe the batter into each donut cavity, filling them about two-thirds full to leave room for rising.
Bake for 10-12 minutes, until the tops spring back when lightly pressed and a toothpick inserted into the thickest part comes out clean or with just a few moist crumbs.
Let the donuts cool in the pan for exactly 5 minutes, then carefully invert the pan onto a wire rack. Tap gently to release the donuts and allow them to cool completely before glazing, about 15 minutes.
For the glaze, warm the Nutella in a microwave-safe bowl for 10-15 seconds until slightly softened. Whisk in the powdered sugar and 2 tablespoons milk until smooth, adding the third tablespoon if needed for a pourable consistency.
Dip the top of each cooled donut into the glaze, letting any excess drip back into the bowl. Return to the wire rack and immediately sprinkle with toasted hazelnuts if using.
Let the glaze set for 10 minutes before serving. The glaze will firm up slightly but remain deliciously soft and glossy.