Mix broccoli, 3/4 of shredded cheese, and rice. In a pan on the stove mix onion, garlic, and butter, cook on low heat 2-3 minutes until onion begins to soften. Add flour to make a paste, cook until bubbly. Add milk all at once, cook until sauce thickens, add salt. Mix sauce with broccoli mixture. Spread remaining cheese over the top. Cook in a 350-degree oven for 40 minutes.