In a 6-qt. stockpot, heat butter over medium heat; saute onion and garlic until tender, 6-8 minutes. Stir in broccoli, carrot, stock, cream and seasonings; bring to a boil. Simmer, uncovered, until vegetables are tender, 10-12 minutes.
Mix cornstarch and water until smooth; stir into soup. Bring to a boil, stirring occasionally; cook and stir until thickened, 1-2 minutes. Remove bay leaves. Stir in cheese until melted.
If using bread bowls, cut a slice off the top of each bread loaf; hollow out bottoms, leaving 1/4-in.-thick shells (save removed bread for another use). Fill with soup just before serving.