Gather all ingredients.

Melt 2 tablespoons butter in a medium stock pot over medium heat. Saute onion and celery until tender.

Add broccoli and broth, cover, and simmer for 10 minutes.

Pour the soup into a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to puree. Puree in batches until smooth and pour into a clean pot. Alternately, you can use an immersion blender and puree the soup right in the cooking pot.

Melt 3 tablespoons butter in a small saucepan over medium to medium-low heat; stir in flour and add milk. Stir until thick and bubbly, and add to soup. Season with pepper and serve.

Serve hot and enjoy!