Coarsely shred the potatoes, zucchini and carrots; drain and pat dry.
Place half of the shredded vegetables and 1/4 cup chopped onion in a food processor or blender; cover and process until finely chopped.
Transfer to a bowl; add eggs, flour, garlic, salt, basil, sugar and remaining onion and shredded vegetables.
In a large nonstick skillet, heat oil. Drop batter by 1/4 cupfuls into skillet, flatten to form patties. Fry until golden brown; turn and cook the second side.