Set a large high-sided skillet over medium heat. Add in the oil and, when hot, add in the carrots and onions and cook until the onions are translucent, 4 to 6 minutes. Add the garlic and cook until fragrant, about 1 minute. Season the mixture with salt and pepper, then add in the ground beef, breaking it up with a wooden spoon. Cook, continuing to break up the meat, until the beef is no longer pink, about 10 minutes.
Add in the tomato sauce, ketchup, molasses, Worcestershire, vinegar, oregano, garlic powder, red pepper flakes, some salt and pepper, and hot sauce as desired. Cook until the sauce thickens up a bit, about 5 minutes. Taste the mixture and season with more salt and pepper as needed.
Spoon the sloppy Joe mixture onto the buns and serve immediately.