Step 1: Prepare the Vegetables

Wash and chop the broccoli and cauliflower into small florets. This helps them cook evenly and blend smoothly into the soup later.

Step 2: Sauté the Aromatics

In a large pot or Dutch oven, melt the butter and olive oil over medium heat. Add the chopped onion and sauté for 3-4 minutes, or until softened and translucent. Add the minced garlic and cook for another 30 seconds, stirring frequently to prevent burning.

Step 3: Cook the Vegetables

Add the broccoli and cauliflower florets to the pot. Stir to coat them in the onion and garlic mixture. Pour in the broth, ensuring the vegetables are fully submerged. Season with salt, pepper, and smoked paprika. Bring the mixture to a boil, then reduce the heat to a simmer. Cover and cook for 15-20 minutes, or until the vegetables are tender.

Step 4: Blend the Soup

Using an immersion blender, puree the soup directly in the pot until smooth and creamy. For a chunkier texture, blend only half the soup and leave some florets intact. If you don’t have an immersion blender, carefully transfer the soup in batches to a countertop blender, then return it to the pot.

Step 5: Add the Cream and Cheese

Stir in the heavy cream and Dijon mustard, mixing well. Gradually add the cheddar cheese and Parmesan cheese, one handful at a time, stirring until fully melted and incorporated. Be sure to keep the heat low to prevent the cheese from clumping or curdling. Taste and adjust seasoning as needed.

Step 6: Serve and Garnish

Ladle the soup into bowls and garnish with your choice of toppings, such as croutons, crispy bacon, or fresh parsley. Serve hot with a side of crusty bread or a green salad for a complete meal.