Preheat grill to 425 to 450 degrees F (220 to 225 degrees C).
In a large mixing bowl, beat eggs, add shredded zucchini and mix well using a fork. Add flour, sugar, salt and vegetable oil and stir to blend well. Finally, add baking powder and mix well using a large spoon. The batter's consistency should be like heavy whipping cream.
Spoon batter on hot grill (about 2 tablespoons) for each pancake. Cook until there are no longer bubbles forming in the pancake about 2 minutes; turn over and cook for 2 minutes longer. Rub pancakes with melted butter and serve immediately.
