In a 4- to 6-quart Dutch oven heat oil over medium-high heat. Add carrots. Cook for 4 to 6 minutes or until browned, turning occasionally. Remove and set aside, reserving oil in pan. Trim fat from meat. Sprinkle meat with salt and pepper. In the Dutch oven, brown roast on all sides in hot oil over medium-high heat. In a small bowl stir together mustard, garlic, and chili powder. Spread over top and sides of browned roast. Add vegetable juice and Worcestershire sauce. Bring to boiling; reduce heat. Simmer, covered, for 1 hour.
Add carrots, beans, chile peppers, and onion to Dutch oven. Return to boiling; reduce heat. Simmer, covered, for 45 to 60 minutes or until meat is tender. Transfer meat to a cutting board and vegetables to a serving platter. Cover each to keep warm.
Bring liquid in Dutch oven to boiling. Boil gently, uncovered, or until reduced to desired consistency (about 1 cup). If necessary, transfer to a measuring cup and skim off the fat. Slice meat and add to platter with vegetables. Spoon sauce over meat and vegetables. Garnish with cilantro and serve with lime wedges and cornbread, if desired.