Begin by heating vegetable oil in a large skillet set over medium-high heat. Once hot, add the cubed beef and sear until browned on all sides, about 3 to 5 minutes. Sprinkle in the chili powder and cumin, stirring constantly to coat the meat and release their aromas, about 1 minute. Next, add the flour and stir well, cooking for another minute to form a light roux. Once fragrant and slightly thickened, transfer the beef mixture into the base of a large slow cooker.
To the slow cooker, add the diced tomatoes, both types of beans, 1 1/2 cups of beef broth, chopped onion, bell pepper, parsley, barbecue sauce, brown sugar, garlic, and salt. Stir everything together until the ingredients are evenly combined and well distributed.
Cover with the lid and set the slow cooker to Low. Cook the chili for 6 to 8 hours, stirring occasionally to prevent sticking and ensure even cooking. The beef should become fork-tender, and the flavors will gradually develop into a hearty, robust chili.
As the chili simmers, check the consistency occasionally. If it begins to thicken too much, stir in a splash of the reserved beef broth to loosen the mixture to your desired texture. Serve hot with your favorite toppings or accompaniments.