Transfer chickpeas to a large bowl. Use a potato masher to mash until mostly broken down, leaving about ⅓ of the chickpeas whole for texture.
Add the, egg, shredded carrots, zucchini, green onions, basil, flour, garlic, lemon juice, cayenne, salt and pepper. Mix gently until combined. Avoid overmixing. If the mixture is too wet, add a tablespoon at a time of flour or bread crumbs until you can shape into a patty.
Using your hands, shape the mixture into patties, about ⅓ cup per patty.
Stovetop Method: Heat olive oil in a skillet over medium-high heat. Cook patties for about 6 minutes per side, until golden brown and heated through.Oven Method: Bake at 400°F for 10 minutes, flip, and bake another 5 minutes.