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, 1/2 teaspoon salt and 1/8 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.