Warm up the milk in the microwave so it is lukewarm. In a small bowl, mix together the milk and yeast. Mix well and leave until you see a few bubbles and it looks foamy.
In the bowl of a stand mixer fitted with the dough hook, mix together the flour, sugar, cinnamon, nutmeg, and salt on your lowest speed.
Add the milk mixture and melted butter to the flour and mix for 2-3 minutes on low. Add the eggs. Turn the speed to medium speed and mix for 3-4 minutes.
Transfer to an oiled bowl and cover with plastic, refrigerate overnight or let it rise for an hour to an hour and a half.
If you had it in the fridge, let it come to room temperature for about 20 minutes
Line a baking sheet with parchment paper.
Roll out the dough on a lightly floured surface until it is about an inch thick. Use a doughnut cutter (or glass!) to cut out the doughnuts. You can reroll the scraps.
Place the doughnuts on the baking sheet and cover with plastic wrap. Let them rise for 30-40 minutes. They're ready when you poke them and it bounces back, leaving just a slight indentation.
While the doughnuts are rising, fill a heavy bottom pot with tall sides with about 4 inches of neutral oil. Let it get to 350°F/175°C over medium heat. Meanwhile, place a cooling rack over some paper towels and fill a shallow bowl with sugar.
Once the oil is hot enough, drop the doughnuts (about 2-3 at a time) in. Turn them just once, about 2-3 minutes for each side. Use a slotted spoon to remove them and place on the cooling rack.
Repeat with all of the doughnuts. After they've been on the cooling rack for a minute or two, roll them in the sugar. Let cool completely.
Filling
Chop up your chocolate and place in a heat proof bowl.
Heat up your heavy cream in a saucepan over medium heat until it is gently simmering. Pour over the chopped chocolate and let it sit for 2-3 minutes.
Use a rubber spatula to mix the two together until smooth. Add in your mascarpone and mix. It may not get completely smooth which is fine.
Place in the fridge for at least 1 hour (you can leave it overnight)
Using a hand held mixer to whip up the mixture for about 1 minute, until very fluffy and pale.
Place into a piping bag and use a a knife to cut a hole in each doughnut. Fill the doughnuts with the chocolate mixture.
Notes
Butter: I use European style butter, like Kerry Gold, in my recipes. This will make your finished loaf much creamier and richer.Oil: Use a neutral oil for frying like vegetable oil, rapeseed oil, or canola oil. When you're finished frying, let the oil cool completely. Do not pour any oil down your sink. Pour it back into the empty container and dispose of it. Storage: These doughnuts are best eaten on the day, but if you need to store them then keep them in your kitchen and cover them with a kitchen towel. I don't recommend putting them in a container as they'll get soggy very quickly.