4 tablespoons unsalted butter 1 medium yellow onion, diced 1 large carrot, diced 2 cloves garlic, minced 1/4 cup all-purpose flour 2 cups half and half 4 cups low-sodium chicken broth 4 cups broccoli florets (from about 1 head) 2 bay leaves 1/4 teaspoon freshly grated nutmeg Kosher salt and freshly ground pepper 1 large russet potato (about 8 ounces) 8 ounces mild yellow Cheddar, shredded (about 2 cups), plus more for serving Melt the butter in a large saucepan or