Melt the butter in a large pot over medium heat.
Add chopped onions and sauté until translucent (about 5 minutes).
Stir in minced garlic and cook for an additional minute.
Add broccoli florets and vegetable broth to the pot.
Bring to a boil, then reduce heat and simmer for 15 minutes.
Use an immersion blender to puree the soup until smooth.
Stir in heavy cream and shredded cheddar cheese.
Season with salt, pepper, and paprika to taste.
Allow the soup to heat through for another 5 minutes.
Serve hot, garnished with fresh parsley and extra cheese if desired.