Step 1: Sauté Aromatics : In a large pot, heat butter and olive oil over medium heat. Add chopped onion and cook for 3–4 minutes until translucent. Add minced garlic and cook for 30 seconds until fragrant.
Step 2: Cook Broccoli Add broccoli florets to the pot and stir to combine. Pour in the vegetable or chicken broth. Cover and simmer for 8–10 minutes until broccoli is tender but still vibrant.
Step 3: Create the Creamy Base : Sprinkle flour over the vegetables and stir well to coat evenly. Cook 1–2 minutes to remove raw flour taste. Gradually add milk or half-and-half, stirring constantly until soup thickens slightly.
Step 4: Add Cheese and Seasoning : Reduce heat to low. Slowly add shredded cheddar cheese, stirring until fully melted. Season with salt, black pepper, and optional nutmeg or smoked paprika. Simmer gently for 2–3 minutes — do not boil after adding cheese.
Step 5: Blend (Optional) : For a smoother texture, use an immersion blender to blend part or all of the soup. Leave some broccoli chunks for texture.
Step 6: Serve : Ladle soup into bowls. Garnish with extra cheddar or chopped herbs if desired. Serve with slices of crusty bread for dipping.