In a large pot, combine the broccoli florets and broth. Bring the mixture to a boil, then reduce heat and simmer for 10-12 minutes, or until the broccoli is tender.

Carefully remove about half of the cooked broccoli with a slotted spoon and set aside. Using an immersion blender, blend the remaining broccoli and broth until smooth, or transfer to a blender and process in batches.

Return the reserved broccoli to the pot. Stir in the shredded cheddar cheese until it is completely melted and the soup is creamy. Do not boil after adding the cheese to prevent it from separating.

Season with salt and pepper to taste, and serve hot.