Stir together flour, zucchini, onion, milk, beaten eggs, and Romano cheese in a large bowl. Season with garlic powder, onion powder, salt, pepper, and parsley. Mix until batter is well combined.
Heat about 1 tablespoon shortening in a large skillet over medium heat. Working in batches, drop 1/4 cupfuls of batter into the skillet and flatten slightly with the back of a spatula. Cook in hot oil until the centers appear dry. Turn over and continue cooking until the other side is golden brown. Transfer to a plate and cover to keep warm. Add more shortening to the skillet as needed.