Heat oil in a large skillet over medium-high heat. Add stew meat and brown for 2 minutes, stirring often. Add chili powder and cumin; cook and stir until fragrant, about 1 minute. Stir in flour and cook for 1 minute more. Transfer meat to a large slow cooker.
Add diced tomatoes, black beans, kidney beans, 1 1/2 cups beef broth, onion, bell pepper, parsley, barbecue sauce, brown sugar, garlic, and salt to the slow cooker; stir until well combined.
Cover and cook on Low, stirring occasionally, until beef is tender, 6 to 8 hours. Thin the chili with remaining beef broth as it cooks, if consistency is too thick.
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