In a large soup pot heat the butter over medium low heat and cook the onion, garlic and a dash of salt and pepper 5 minutes, stirring often.

Add the broccoli, broth, mustard, ½ teaspoon salt and ⅛ teaspoon black pepper.

Turn the heat up and bring it to a simmer. Cook 20 minutes, stirring often.

Stir in the half and half and bring to a simmer again for 5 - 10 minutes.

Turn heat down to low and add the cheddar, stir until completely melted. Stir in the Parmesan. Season to taste with more salt and pepper if needed.