Bring the quinoa and water to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the quinoa is tender and the water has been absorbed, about 15-20 minutes.
Roughly mash the black beans with a fork leaving some whole black beans in a paste-like mixture.
Mix the quinoa, bread crumbs, bell pepper, onion, garlic, cumin, salt, pepper, cheese, and egg into the black beans using your hands.
Form the black bean mixture into 6 patties.
Heat the olive oil in a large skillet.
Cook the patties in the hot oil until heated through, 2 to 3 minutes per side.
Notes
Patties can also be baked in a 400°F oven for 20-30 minutes.