In a small bowl, mix together the yeast and warm milk.
Let rest until frothy, about 5-10 minutes.
While the yeast is resting, in the bowl of a stand mixer fitted with a dough hook, mix together the eggs, melted butter, and sugar, until well incorporated.
Add the frothy milk and yeast mixture to the mixer bowl, and mix until well incorporated.
Add the flour to the bowl, and top with the salt. Mix until well incorporated. Then continue to let the mixer knead for an additional 5 minutes on low speed.
Remove the dough from mixing bowl, and grease the mixing bowl with some of the oil. Return the dough to the bowl and cover. Allow the dough to rise in a warm area for an hour.
After an hour has elapsed, remove the dough from the bowl and punch it down.
Roll the dough out to a 1/4 inch thickness.
Using the 1 inch cutter, cut as many circles from the initial roll of the dough as possible. The more you re-roll it the tougher the dough will become.
Let the cut circles of dough rise again for another 50 minutes to an hour, covered in a warm place.
The last twenty minutes that the dough is rising, heat the oil in a dutch oven or fryer until it reaches 375°F.
Line plates or cooling racks with paper towel to absorb the grease of the fried doughnuts, and set aside.
Mix together the cinnamon and sugar and put into a plastic or paper bag. Set aside.
Fry the dough in batches, taking care not to overcrowd the frying oil. About 1 minute on one side, flip, and one minute on the other side.
Move each cooked batch to the paper towels.
When all doughnuts have been cooked. Place in the bag of cinnamon sugar in batches, and shake to coat.
Remove the coated doughnuts from the bag and serve while warm.