Preheat the oven to 400 degrees Fahrenheit.
Blanch broccoli - bring 4 quarts of salted water to a boil. Once boiling, place broccoli in the water and boil for about 4 minutes. Remove broccoli from water and set aside.
Melt butter over medium heat in a large ovenproof skillet. Add onions and mushrooms and sauté for about 5 minutes.
Sprinkle flour over the onions and mushrooms and stir. Cook for about 2 minutes.
Slowly stir in the chicken broth, making sure to get up all the brown bits in the bottom of the skillet. Slowly stir in the evaporated milk, mustard powder, salt, black pepper, and garlic powder. Bring mixture to a simmer and allow to simmer for about 5 minutes, stirring often.
Remove skillet from heat and slowly whisk in 2 cups of the grated cheese, until the cheese has melted and the mixture is smooth and creamy. Stir in the broccoli and rice. Sprinkle the remaining cheese over the mixture.
Place in the preheated oven and bake for 15 minutes, until the cheese on top has melted. Remove and enjoy :)