First, dissolve the yeast in the lukewarm water, and allow it to sit until it blooms.
In the bowl of a stand mixer fitted with a dough hook, combine all ingredients except for one of the whole eggs, and beat on medium speed for 5 minutes, then high speed for 5 more minutes.
Add in the remaining egg, and beat on medium speed until a smooth and elastic dough forms {you may have to add a little more flour if it seems too sticky}.
Knead by hand for a couple of minutes, then place the dough in a large, lightly oiled bowl, cover with plastic wrap, and allow to rise in a warm place for at least 2 hours until tripled in size.
After the first rise, lightly knead the dough, roll it out to 1.5 cm/0.5 inch thickness, and cut out rounds. I found a regular water glass to be the perfect size!
Transfer all your rounds to baking sheets lined with wax paper, spray lightly with water, and cover with plastic wrap or a tea towel. Allow the bomboloni to rise another hour and a half until they triple in size once more.
When ready to fry, heat vegetable oil in a large, deep pan to a temperature between 170-180C {a frying thermometer comes in handy}.
Fry the bomboloni a few at a time, making sure to not crowd the pan. Fry them for about 3 minutes on each side, until they are golden brown, then drain off the excess oil, and set them on a wire rack to cool.
While they are still warm, pour some granulated sugar in a small bowl, and roll the bomboloni around until completely coated in the sugar.
Fill as desired {I have included a link to the chantilly cream below}, and enjoy!
*NOTE* I have read that you can also bake these at 350F for about 20 minutes instead of frying (but I have not personally tried it).