Bring broth, olive oil, garlic powder, onion powder, and salt to a boil in a medium saucepan that has a lid.

Stir in the white rice and broccoli, bring back to a boil, cover with the lid, and turn heat down to low.

Let simmer for 20 minutes until the rice is cooked through and the broccoli is tender; if there is a little broth left in the pan that's fine.

Mix in the cheddar cheese until melted and add a splash of half and half for a creamier sauce.

Taste and add more salt and pepper as needed.