In a large pot over medium heat, melt butter. Add onion and celery and cook until soft, 5 minutes. Add garlic and cook until fragrant.
Whisk in flour and let cook 1 minute. Slowly add chicken broth and season with salt and pepper.
Stir in broccoli and carrots. Bring to a boil and reduce heat to low. Let simmer until vegetables are tender, 20 minutes.
Slowly add cream and bring to a simmer, then stir in cheddar.
Season with salt and Bayou City Garlic Pepper and top with more cheddar. Serve with French bread.