Put drained chickpeas into a large bowl and mash with a potato masher, or the back of a heavy spoon, until broken down but still a bit chunky. Set aside.
Heat 1 Tbsp oil in a skillet over medium-high heat. Add the onion, carrots and salt. Cook, stirring occasionally, until softened, about 5-6 minutes. Add the zucchini, red pepper, garlic and cumin or curry powder. Cook, stirring often, for 2 more minutes. Add skillet mixture to the bowl of mashed chickpeas and stir to combine.
Add the egg, parsley and black pepper to the bowl. Mix all together well. Form five 1-inch thick burgers or 10 sliders from the mixture.
Wipe skillet with a paper towel and heat another 1 Tbsp oil over medium heat. Add the burgers. Cook, turning once, until golden brown and heated through, about 4 minutes on each side.