Trim and shred zucchini. Place in a colander or sieve and let drain for 15 minutes, gently pressing zucchini occasionally to extract moisture. Spread on paper towels; blot to remove moisture. Measure 5 cups shredded zucchini.
In a large mixing bowl, beat eggs. Stir in flour, Parmesan cheese, onion, salt, black pepper and garlic powder, if you like, till just moistened (batter should be lumpy). Stir in shredded zucchini till just combined.
For each zucchini pancake, spoon a generous 1 tablespoon of batter on a hot, lightly oiled griddle or heavy skillet, spreading to form a 4-inch circle. Cook over medium-low heat for 1-1/2 to 2 minutes on each side or till the pancake is golden brown. Season the pancakes with some additional salt and black pepper to taste, if you like. Makes 24 appetizers or 8 side-dish servings.