In a large heavy bottom stockpot, melt 4 tbsp of butter over medium heat
Add onion and cook until soft, about 4 minutes
Add garlic and cook about 1 minute longer
Add flour to the pot, mix and cook until the rawness of the flour is gone, about 2 minutes
Whisk in chicken stock and mix well until there are no lumps of flour
Slowly whisk in half and half
Add broccoli, carrots, paprika, and mustard powder. Season with salt and pepper
Simmer over medium heat for about 25 minutes or until broccoli and carrots are fork tender
Turn off heat. At this point, you can blend with an immersion blender for a fine texture soup, or leave broccoli whole for a chunkier soup. I like to blend most of the soup and leave some larger pieces.
Add the FRESHLY shredded cheddar cheese to the soup over low heat and blend well.
Check seasonings and add salt and pepper if needed. Serve immediately
Notes
Shred your cheese to use in the soup to create a creamy, smooth consistency. Using prepackaged shredded cheese may form clumps and will not melt consistently.