I sprinkle the yeast and a teaspoon of sugar over the warmed milk and give it a gentle stir. I let this sit for about ten minutes until it turns foamy on top. If it doesn't foam up, my yeast is usually dead, and I start over with a fresh packet.
I add the flour, sugar, salt, and vanilla into my stand mixer bowl fitted with the paddle attachment. Once the yeast mixture looks bubbly, I pour it in along with the softened butter and eggs. I knead everything on medium speed for about five minutes until the dough turns smooth and pulls away from the bowl.
I turn the dough out onto a floured surface and roll it to about half an inch thick. Using my biscuit cutter, I cut out round donuts and set them a couple of inches apart on a floured baking sheet. This spacing keeps them from sticking together as they rise.
I sprinkle a little flour over the tops of the cut dough and cover them with a clean, lint-free kitchen towel. I place the tray somewhere warm and let it rise for about an hour and a half, until the rounds look noticeably puffier.
I heat vegetable oil in a heavy pot to 350°F, filling it only halfway up the sides for safety. I fry the donuts in small batches until they turn a deep golden brown on both sides, then I lift them out with a slotted spoon onto paper towels to drain.
While the bomboloni are still warm, I roll them in granulated sugar so it sticks well. Then I load my piping bag with Nutella and push the tip into the side of each donut, filling it until I feel a little resistance, which tells me it's generously stuffed.