Preheat your oven to 425°F (220°C). Toss the chopped broccoli florets with 1 tablespoon of olive oil and a pinch of salt and pepper. Spread them evenly on the baking sheet. Roast for 20-25 minutes, turning halfway through, until the edges are golden and slightly crispy.
While the broccoli roasts, heat the remaining tablespoon of olive oil in your large pot over medium heat. Add the chopped onion and cook, stirring occasionally, until translucent and soft, about 5 minutes. Add the minced garlic and paprika, cooking for another minute until fragrant.
Pour in the vegetable broth and bring it to a gentle boil. Reduce the heat and let it simmer for about 10 minutes to let the flavors meld.
Add the roasted broccoli to the pot. Use an immersion blender to puree the soup until smooth and creamy. If you don’t have an immersion blender, carefully transfer the soup to a regular blender in batches, then return it to the pot.
Stir in the heavy cream and shredded cheddar cheese over low heat. Continue stirring until the cheese has melted completely and the soup is velvety. Taste and season with extra salt and pepper as needed.
Ladle the soup into bowls and enjoy immediately. For an extra touch, garnish with a sprinkle of cheddar, a dash of paprika, or some crunchy croutons.
