Combine broccoli, broth, and quinoa in a saucepan; bring to a boil. Reduce heat to medium-low, place a cover on the saucepan, and cook at a simmer until the broth has been absorbed and the quinoa is tender, 15 to 20 minutes.

Stir Cheddar cheese into the quinoa, replace the lid, and set aside until the cheese melts, 2 to 3 minutes; season with salt and pepper.