In a large skillet over medium heat, melt the butter and add the olive oil. Add the chopped onion and garlic, sautéing until the onion becomes translucent, about 3-4 minutes.
Onion and garlic sautéing in a skillet
Add the broccoli florets to the skillet and cook for an additional 5 minutes, until they are bright green and slightly tender.
In a large mixing bowl, combine the cooked rice, sautéed vegetables, 1 cup of cheddar cheese, milk, sour cream, salt, pepper, and paprika. Stir until well mixed.
Broccoli rice casserole mixture in a mixing bowl
Transfer the mixture into a greased 9×13-inch casserole dish, spreading it evenly.
Sprinkle the remaining 1/2 cup of cheddar cheese and the Parmesan cheese over the top.
Unbaked casserole topped with shredded cheese
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and bubbly.
Remove from the oven and let it cool for a few minutes. Garnish with fresh parsley before serving.