Almost-Famous Broccoli-Cheddar Soup

INGREDIENTS

• Kosher salt and freshly ground pepper
• 1/4 cup all-purpose flour
• 3 cups low-sodium chicken broth
• 1 small onion, chopped
• 2 1/2 cups (about 8 ounces) grated sharp white and yellow cheddar cheese, plus more for garnish
• 2 cups half-and-half
• 1/4 teaspoon freshly grated nutmeg
• 4 7-inch sourdough bread boules (round loaves)
• 6 tablespoons unsalted butter
• 4 cups broccoli florets (about 1 head)
• 2 bay leaves
• 1 large carrot, diced