Cheesy broccoli soup

1/4 cup butter
1/2 cup chopped onion
2 garlic cloves, minced
4 cups fresh broccoli florets (about 8 ounces)
1 large carrot, finely chopped
3 cups chicken stock
2 cups half-and-half cream
2 bay leaves
1/2 teaspoon salt
1/4 teaspoon pepper
1/4 cup cornstarch
1/4 cup water or additional chicken stock
2 1/2 cups shredded cheddar cheese

Optional toppings: crumbled cooked bacon, additional shredded cheddar cheese, ground nutmeg and pepper

In a 6-quart stockpot, heat butter over medium heat; sauté onion, carrot and garlic until tender, 6-8 minutes. Stir in stock and seasonings; bring to a boil. Simmer another 10-12 minutes. Add 3/4 cup cream and bring to a boil. Cook broccoli until tender crisp in separate pan. Mix remaining cream and cornstarch until smooth; stir into soup. Bring to a boil, stirring occasionally. Cook and stir until thickened, about 1-2 minutes. Remove bay leaves. Stir in broccoli and let cool just a bit and then stir in cheese until melted. If desired, serve soup with toppings.