Melt butter in a large Dutch oven over medium heat; add carrots and next 4 ingredients; sauté 8 minutes or until onion is tender. Stir in chicken broth. Bring to a boil over medium-high heat. Reduce heat to medium, and simmer, stirring often, 20 minutes. Stir in rice, and cook, stirring often, 18 minutes or until rice is tender.
Remove from heat. Process mixture with a handheld blender until smooth. Stir in half-and-half, if desired. Serve with desired toppings.