In a large skillet, heat oil over medium-high heat. Add onion, peppers and carrot; cook and stir until crisp-tender, 6-8 minutes. Add garlic; cook 1 minute longer., Add broth and lentils; bring to a boil. Reduce heat; simmer, uncovered, until lentils are tender, about 15 minutes, stirring occasionally. Stir in chopped tomatoes, tomato sauce, chili powder, mustard, vinegar, Worcestershire sauce, honey, tomato paste, salt and pepper. Bring to a boil. Reduce heat; simmer until thickened, about 10 minutes. Serve on buns.