In a large saucepan over medium heat, stir together stock, onions, broccoli and garlic for about 5 minutes.
Once it comes to a low boil, cover and let simmer for 10 minutes.
Stir in the heavy cream and continue to cook for 3-5 minutes.
Stir in cheeses, until smooth (about 1-2 minutes). Season with salt and pepper, to taste.
Serve immediately.