Thinly slice the beef eye of round, or ask your butcher to do it for you.
Crack the eggs into a bowl and beat well with a fork. Finely mince the garlic and parsley, then add them to the eggs along with the grated cheese and a pinch of salt. Mix until thoroughly combined.
Place the meat slices into the egg mixture and allow them to marinate for about 30 minutes to absorb the flavors.
Pour the breadcrumbs onto a flat plate. Turn the meat in the egg mixture once more, then coat each slice in the breadcrumbs—taking care to keep the minced garlic and parsley on the meat—pressing firmly so the coating adheres completely.
Once all the cutlets are breaded, pour the olive oil into a large skillet and heat it. When the oil is hot, fry a few slices at a time over medium-high heat so the meat browns nicely without absorbing excess oil.
When the cutlets are golden brown on both sides, remove them with a slotted spoon, drain on paper towels, and season lightly with salt.
Serve hot alongside french fries or a fresh seasonal salad.