Bring a pot of oil to 370 degrees F on a candy thermometer. The oil should be about 3 inches deep and not come up more than halfway up the side of the pot.
Roll out the dough to about 1/4-inch thick rectangle. Cut the rectangle into 16 equal portions.
Mix together the ricotta, nutmeg, oregano, salt and pepper. Put about a tablespoon of the filling onto the dough, placing it so that you can easily close the dough around it. Brush the edge of the dough with water.
Press the dough closed around the filling. Making sure that the dough is sealed well, so the filling won’t come out while it is frying.
Place the doughnuts in the hot oil for about 2 minutes, or until they are golden brown. Put only a few doughnuts in the oil at a time, they should not be crowded or they will not fry evenly.
Flip the doughnuts over and fry the second side for another 2 minutes. Make sure your oil is staying around 370°F.
When the doughnuts are done frying, use a basket skimmer to remove them from the oil and place them on paper towels to drain the excess oil.
Serve with the tomato sauce or pesto sauce.