In a large pot, melt the butter over medium heat. Add the chopped onion and garlic, sautéing for about 3-4 minutes until the onion becomes translucent.
Add the broccoli florets to the pot and stir for another 2 minutes.
Pour in the vegetable broth and bring to a boil. Reduce heat, cover, and let it simmer for about 10 minutes until the broccoli is tender.
Use an immersion blender to puree the soup until smooth. If using a traditional blender, allow the mixture to cool slightly, then puree in batches.
Return the pureed soup to the pot. Stir in the heavy cream and bring to a gentle simmer.
Add the shredded cheddar cheese gradually, stirring until it is completely melted and incorporated.
Season the soup with salt, black pepper, and paprika. Adjust seasonings to taste.
Serve hot, garnished with croutons if desired.