Preheat oven to 350°F and butter a 9x13 baking dish evenly on the bottom and sides.
Cook the long grain white rice according to package directions and set aside.
Steam the broccoli florets according to package directions and set aside.
In a large mixing bowl, combine the cooked rice and steamed broccoli.
In a medium bowl, mix together the diced onion, cream of mushroom soup, cheddar cheese soup, whole milk, seasoned salt, garlic powder, and black pepper until fully combined.
Pour the soup mixture over the rice and broccoli, gently folding to coat without breaking the broccoli too much.
Spread the mixture evenly into the prepared baking dish.
Top with shredded mild cheddar cheese.
Bake for 30 to 35 minutes until the cheese is melted, lightly golden, and bubbly around the edges.
Remove from oven and let rest at room temperature for 5 minutes before serving.