Preheat the oven to 375 degrees.
In a microwave safe bowl, place the broccoli florets in with 1-2 tablespoons of water. Salt and pepper the broccoli. Steam in the microwave for 5-6 minutes or until the broccoli is tender.
Stir the cooked rice into the bowl with the steamed broccoli. Salt and pepper to taste.
In a small bowl mix together the gluten-free flour, garlic powder, thyme, and cayenne.
In a Dutch oven, melt 3 Tbs of butter over medium heat. Stir in the flour mixture and whisk to combine.
Slowly whisk in the milk. Be sure to break up any clumps of flour as you continue to stir. Once the mixture begins to bubble, remove from heat.
Stir in 1 1/2 cups of grated cheese until melted.
Pour the cheese mixture into the rice and broccoli. Salt and pepper to taste.
In an 8x8 casserole dish, pour in the broccoli and cheese mixture. Use a spoon to smooth the top. Pour the remaining 1/2 cup of cheese over the top of the casserole.
Sprinkle the cornflakes over the top.
Pour the melted butter over the top.
Bake for 30 minutes.
Remove from the oven, allow to rest for 10 minutes.
Serve.