1. Melt butter in a Dutch oven over low heat; add carrot, onion, and garlic. Sauté until tender. Stir in chicken, chicken broth, green chiles, cumin, and red pepper; bring to a boil over medium-high heat. Reduce heat, cover, and simmer 20 minutes.
2. Place beans in a medium bowl, and mash using a potato masher until about half the beans are still whole. Add beans and whipping cream to chicken mixture. Cook 10 minutes over medium heat, stirring frequently, until thickened and hot. Stir in cilantro, if you'd like.