Place flour in a sealable plastic bag. Seal and shake to cover inside of bag.
Add mozzarella pieces to bag. Shake to coat each piece with the flour (Add more flour, if needed, to fully coat). Remove from bag.
Place eggs in a shallow bowl and beat slightly.
Place breadcrumbs in another shallow bowl.
Dip a slice of mozzarella, individually, into the beaten eggs. Turn to coat fully.
Remove from eggs, allowing excess to drip off and place in breadcrumbs. Turn to coat completely, pressing lightly to make sure the breadcrumbs stick.
Place on a rack to dry. Repeat with remaining slices of mozzarella, adding (and beating) more eggs and breadcrumbs, if needed.
When all pieces are dry, repeat above process - dip breaded pieces, one at a time into the beaten eggs again and then into the breadcrumbs, to apply a second coating, adding (and beating) more eggs and breadcrumbs, as needed.
Again, place on a rack and allow to dry.
Fill a small saucepan with the olive oil to about 1 1/2 inches from the top.
Place over medium heat and heat to deep frying temperature.
Fry breaded mozzarella slices, a few at a time, until they are deep brown.
Remove to a paper towel-covered plate to drain. Continue until all pieces are fried.
Arrange finished slices on a serving plate or plates.
Add a light dusting of Romano cheese.
Scatter basil over top.
Pour a small bit of chosen warmed tomato sauce over top and serve with remainder in a bowl or bowls for dipping.