Melt the butter in a large pot over medium heat.
Add the chopped onion and sauté until translucent.
Stir in the minced garlic and cook for an additional minute.
Add the broccoli florets and vegetable broth to the pot.
Bring the mixture to a boil, then reduce heat and simmer for 15 minutes.
Using an immersion blender, purée the soup until smooth.
Stir in the heavy cream and shredded cheddar cheese.
Season with salt, pepper, and paprika to taste.
Simmer for another 5 minutes to allow flavors to meld.
Serve hot, garnished with croutons if desired.