Heat the milk slightly and dissolve the yeast with 1 tbsp sugar in it. Leave it to bubble in a warm area.
Sift the flour in a bowl and form a well. Put the eggs and 2 types of sugar in it. Knead a dough, gradually add the softened butter (divided into 4 parts beforehand) to it. Knead until the butter is fully absorbed and you get a smooth and stretchy dough.
Place the dough in a buttered bowl, cover with a towel and leave it to rise in a warm area for 2 hours.
Once the dough doubles in volume, transfer it to a floured counter. Roll it out into a sheet about 1/2″ (1 cm) thick. Cut out circles with a glass about 2 3/4″ (7 cm) in diameter. Knead the leftover dough again and repeat the process until out of dough.
Arrange the cut out circles onto an oven dish covered with greased baking paper. Put greased plastic wrap on top, to prevent a crust from forming. Let them rise again for about 2 hours.
Heat oil to 329°F (165 °C) in a suitable container.
Prepare 2 plates - put paper towels in one of them, where you're going to place the ready bomboloni in, and sugar for rolling in the other one. Fry 5-6 of them at a time, no more, to make sure that they fry evenly.
Fry until golden on both sides. They turn golden very quickly and should not be left unsupervised.
Take them out and drain on the paper towels, then immediately roll in sugar.
You can eat them as is or fill them with a cream or marmalade of your choice.