Heat the milk to 110 degrees F and stir in yeast and sugar. If using active dry yeast, allow to sit for 15 minutes. If using instant yeast, simply move on to the next step.
Mix the eggs and vanilla into the milk yeast mixture.
Combine flour and salt together in the bowl of a stand mixer fitted with a dough hook.
Pour the wet ingredients into the flour and mix on low-medium speed for about 3 minutes, or until it forms a ball around the hook.
Add in one piece of butter at a time, allowing it to fully incorporate before adding the next.
Once all of the butter is incorporated, turn the mixer up to medium-high speed and mix for 6-8 minutes. To check if the dough is ready, tear off a small piece and carefully spread it out to see if you can see the light through it without it tearing. If it tears, mix for another minute and check again.
Once the dough is ready, transfer it to a lightly greased bowl, cover, and allow to proof overnight in the fridge. Alternatively, you can let the dough rise in a warm place for about 1 hour or until doubled in size.
Divide the dough into 12 equal pieces about 50g each. Flatten each piece out and fold the edges over into the center, then turn it over and roll into a smooth ball.
Place each ball onto a parchment lined baking sheet spaced about 3 inches apart, then cover and allow to rise for about 30 minutes.
Meanwhile, preheat the oven to 350 degrees F.
Once the brioche has risen, brush each one with an egg wash and bake for 10 minutes or until they are golden and they reach 190 degrees F on an internal thermometer.
Once the donuts are cool enough to handle, toss each of them in granulated sugar and place bake on the baking sheet to cool completely.
Using a chop stick or something similar, poke a hole into each donut and move it around to create some room.
Fill a piping bag with a small round piping tip with the Nutella, and fill each donut.
Serve these donuts the day they are baked and enjoy!