Heat a large skillet sprayed with cooking spray over medium-high heat.
Stir zucchinis, onion, carrot, garbanzo bean flour, onion soup mix, and egg whites together in a bowl until well mixed. Divide zucchini mixture into 6 equal portions and shape into large patties.
Pan-fry zucchini patties in the hot skillet until brown and crispy, about 3 minutes per side.
Place mayonnaise, water, paprika, onion powder, garlic powder, and basil in a food processor; pulse until mixture is smooth. Drizzle over zucchini pancakes to serve.
