Cook broccoli and rice separately according to package directions. Set aside.
Melt the butter in a large pot over medium heat. Sauté the onion until tender, about 5-7 minutes.
In a separate saucepan, combine the soup, milk and Velveeta cheese. Heat over medium heat until the Velveeta is melted and the sauce is smooth.
Add the broccoli, rice and cheese sauce to the onion in the stock pot. Stir until all the ingredients are evenly combined. Season with salt and pepper.
Spread the broccoli mixture into an even layer on the bottom of a greased 9 x 13 x 2-inch casserole dish.
Top the casserole with the shredded cheese.
Bake for 30-35 minutes until the casserole is bubbly and the cheese is melted.
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Notes
Make ahead. Cheesy broccoli casserole can be made up to 24 hours in advance. The casserole will need to be covered and stored in the refrigerator. Allow the casserole to come to room temperature before cooking or cook for an additional 5-10 minutes.Storage. Leftover broccoli casserole needs to be stored in an airtight container within two hours of baking. Consume within four days.Freezing. Broccoli casserole can be frozen either baked or unbaked. Cover the storage container with a lid or aluminum foil. Store on a level surface. Allow the casserole to thaw overnight in the refrigerator. Allow the casserole to come to room temperature before cooking or cook for an additional 5-10 minutes.Reheating. Individual servings of broccoli casserole can be reheated in the microwave. If reheating a larger portion, preheat the oven to 250 degrees and bake, covered, for 45 minutes to one hour until heated through.