In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Add the minced garlic and sauté for an additional 1-2 minutes until fragrant.
Stir in the broccoli florets, vegetable broth, and mustard powder. Bring the mixture to a boil, then reduce the heat and simmer for about 15 minutes, or until the broccoli is tender.
To thicken the soup, sprinkle the flour over the mixture and stir continuously for 2-3 minutes. This will help prevent any lump formation.
Using an immersion blender, carefully blend the soup until smooth. (Alternatively, you can blend in batches using a regular blender. Just be cautious of the hot liquid.)
Return the soup to medium heat and stir in the heavy cream and shredded cheddar cheese. Continue stirring until the cheese is melted and the soup is smooth.
Season with paprika, salt, and pepper to taste.
While the soup is heating, prepare the bread bowls by cutting the top quarter off each bread bowl and hollowing out the insides, leaving about an inch of bread all around.
Ladle the hot cheddar broccoli soup into each bread bowl.
Garnish with fresh parsley if desired, and serve immediately.
Notes
Serve the bread bowls on a wooden board with the tops arranged artfully alongside. If desired, place some extra cheese on top of the soup before serving for a cheesy finish!