Preheat oven to 350 degrees F.
Bring a 3-quart saucepan two-thirds full of water to a boil over high heat. Add broccoli and blanch for 2 minutes. Drain and set aside.
Return the saucepan to medium-high heat and melt butter. Add diced onion and cook for 5 to 7 minutes, until translucent.
Add flour and stir to combine, reducing heat to medium. Cook for 1 minute. Pour in milk one cup at a time, stirring until smooth after each addition.
Increase heat slightly and stir in garlic powder, smoked paprika, mustard powder, salt, and pepper. Stir continuously until the sauce thickens, about 5 minutes.
Turn off heat. Stir in cream cheese and three-quarters of the shredded cheddar until fully melted and smooth. Fold in the cooked rice and blanched broccoli.
Transfer to a 2-quart baking dish. Top with the remaining cheddar. Bake for 25 to 30 minutes, until bubbly with crispy edges.
Broil for 2 to 3 minutes to brown the top, if desired. Let rest 10 minutes before serving.