Broccoli Cheese Soup

INGREDIENTS

• 1 1/3 cup all-purpose flour
• 1 cup chicken broth, optional
• Salt and freshly ground black pepper
• 3 cups grated cheese (mild Cheddar, sharp Cheddar, Jack, etc.), plus more for garnish, optional
• Olive oil, for drizzling
• 4 heads broccoli, cut into 1-inch florets
• 2 cups half-and-half
• 4 cups whole milk
• Pinch nutmeg
• 1 whole onion, diced
• 1 stick (4 ounces) unsalted butter