If using fresh vegetables, trim and cut them into bite-sized pieces, then parboil them until tender, drain and let them cool. If using frozen vegetables, let them defrost.
Roll the vegetable pieces in flour, then dip them in a mixture of eggs beaten with finely chopped parsley, salt, pepper and just a bit of grated pecorino cheese.
Shallow fry the vegetables gently in olive oil ('light' olive oil will do here) until they turn a light golden brown. The oil should be about 1/2 inch (1 cm) or so deep, or enough to come about halfway up the pieces. Make sure that the oil is just hot enough so that it gently bubbles around the pieces as you place them into the pan. If the oil is not hot enough, the vegetables will turn out greasy; too hot and the egg batter will brown before the insides of the vegetable pieces are fully cooked. You'll need to fry a few pieces at a time, as many as will fit comfortably in your frying pan without crowding. (If you crowd them, they will steam, and get soggy and greasy.)
You then drain the vegetables, either on a plate lined with paper towels or—my preferred method—on a cooling rack placed over a baking sheet to catch the oil and stray bits of batter. Keep your already fried vegetables warm in the oven while you are frying the rest.
Sprinkle the fried vegetables with salt and serve either hot or at room temperature, with lemon wedges if you like. I promise, they're addictive!