Drain and rinse chickpeas. Finely chop broccoli. Bring a pot of water to a boil.
Add chickpeas and broccoli to the boiling water and cook for about 2 minutes, until soft. Drain and add to a large bowl.
Using a fork, mash chickpeas and broccoli slightly. They should form a paste-like consistency, with whole pieces still intact throughout.
Add egg, flour, cheese, onion powder, garlic powder and salt and pepper to taste to the bowl. Mix well until combined.
Using your hands, form the mixture into 8 patties. Set aside.
Add olive oil to a pan over medium heat. Once oil has spread, add patties to the pan and cook for about 3-5 minutes on each side, until golden and cooked through. Serve immediately.