In a large pot over medium heat, melt the butter and add the olive oil. Sauté the diced onion and celery for about 3 minutes until they begin to soften. Stir in the minced garlic and cook for another 30 seconds, just until fragrant.

Add the broccoli florets to the pot, followed by the chicken broth, paprika, dried Italian herbs, salt, and pepper to taste. Increase the heat to bring everything to a boil, then reduce the heat to a simmer. Let the soup cook for about 10 to 12 minutes, or until the broccoli is tender.

For a chunkier soup, carefully remove a few broccoli florets from the pot and set them aside. Use a hand immersion blender or transfer the soup to a blender or food processor and blend until smooth and creamy. I find that blending makes the soup especially velvety—just be careful with hot liquids.

Return the blended soup to the pot if needed. Stir in the shredded cheddar cheese and reserved broccoli florets (from Step 3) until the cheese is fully melted and the soup is well mixed. Taste and adjust seasoning if necessary.

Ladle the soup into bowls and sprinkle with chili pepper flakes for a bit of extra heat. Serve hot and enjoy!