Preheat oven to 350 degrees. Cook rice according to directions, set aside.
In a large pot, cover broccoli florets with water and a pinch of salt, bring to a boil, cook until tender (about 6-8 minutes), drain and return to pot, set aside.
In a large saucepan over medium heat, sauté onions in butter, until soft and translucent. Add soups and Velveeta cheese, cook until the cheese has melted.
Add the cooked rice and soup mixture to the broccoli pot. Stir until everything is well combined. Add a little milk if mixture is too thick.
Pour broccoli rice and cheese mixture into a buttered 9x13 baking dish and top with shredded cheddar cheese and season with pepper, if desired. Bake the casserole for 25-30 minutes or until cheese is melted and golden brown.
Cook's Note: You can substitute frozen broccoli florets for fresh broccoli.