Cook rice as instructed on the package and set out a large, greased 9x13 baking dish.
Briefly boil 5 cups broccoli florets for 1-2 minutes, then cool under cold running water, strain, and set aside.
Preheat oven to 350°F.
In a large pan over medium-low heat, cook 3 tbsp salted butter and 1 cup diced onion until soft, stirring regularly, about 5 minutes.
Whisk in 3 tbsp flour, 1/2 tsp garlic salt, and 1/4 tsp pepper; stir for a couple minutes until well combined.
Raise heat to medium and whisk in 2 cups milk while pouring; stir for 3-5 minutes as it bubbles until reduced by about half.
Remove the sauce from heat and whisk in 1/4 tsp dry mustard, 1/4 tsp paprika, 2 oz cream cheese, and 1.5 cups cheddar cheese; stir until the cheese is melted and the sauce is smooth.
Add the cheese sauce, 2 cups cooked white rice, and the blanched broccoli to the baking dish and stir to combine. In a small bowl, mix 2 tbsp melted butter, 1/2 cup panko bread crumbs, and 1/2 tsp Italian spices; add 1/2 cup cheddar cheese and mix again to make the topping.
Top the casserole with the panko-cheddar mixture and bake uncovered for 30-45 minutes, until the cheese is bubbling and the topping is golden brown. Sprinkle with 1 tsp fresh chopped parsley before serving.