To make the dough: Pour the milk into the bowl of a stand mixer. Stir in the yeast. Add the eggs, sugar and salt, stir to combine. Dump in the flour and using the dough hook attachment, mix the dough on low speed until it comes together in a shaggy ball. While the dough is mixing, drop in the room temperature butter a bit at a time.
Once the butter is added, turn the mixer up to medium high and mix the dough for 3 minutes, more if you can still see chunks of butter.
Scrape down the bowl, cover with plastic and allow the dough to double in size, about 2 hours.
To make the doughnuts: Mix together the brown sugar, sugar and cinnamon in a small bowl. Set aside.
Pour the dough out onto a well floured surface. Shape the dough into a round and divide the dough into 12 pieces, cutting it like a pizza with a bench scraper.
Form each piece into a ball. Cover with plastic and let rest until doubled in size, about 2 hours.
In a heavy-bottomed medium pot, heat about 3 inches of oil over medium heat until it reaches 360°F on a thermometer. Line a plate with paper towel. Once the oil it hot, carefully slide the dough into the oil. Only put a couple in at a time, so they have plenty of room to float. Allow to fry for about 2 minutes, then flip them over to cook the other side. See my video for tips on frying. Drain the doughnuts on the paper towel for a minute, then dredge the doughnut in the vanilla sugar. Repeat with the rest of the dough.
Fill with whatever filling you like. Once the doughnuts have cooled slightly, pierce the doughnut with a paring knife, creating a pocket for the filling. Use a pastry bag with a Bismarck tip (make sure it is big enough for any fruit to fit through). Fill each doughnut.
You can dip the doughnuts in ganache if you need a little something extra or drizzle with glaze instead of the cinnamon sugar. You can even let people fill and top their sufganiyot however they please!