Slowly add in half & half, about 1 cup at a time then add in broth/stock, 1 cup at a time, stirring well between adding to dissolve any chunks. Stir in chopped carrots, broccoli, garlic/onion mixture and seasoning and simmer for 30-40 minutes. Once vegetables are soft, stir in shredded cheese and allow to melt before serving in a bowl. Serve with french bread.