Heat oil and butter in a large skillet over medium-high heat. Add onions and salt and cook, stirring occasionally, for 10-12 minutes or until soft and caramelized. Add bell peppers and cook for 3-4 minutes. Add garlic and mushrooms and cook, stirring occasionally, for an additional 3-4 minutes. Transfer cooked vegetables to a large bowl and set aside.
Return skillet to burner and increase heat to high. Add ground sirloin and cook, breaking up meat with a spoon or spatula, until meat is cooked through and no longer pink, about 5-6 minutes. Season meat with Stubb's Steak Spice Rub. Add cooked vegetables to skillet with browned meat. Stir in Stubb's Sweet Black Pepper Anytime Sauce and ¾ cup beef broth. Reduce heat to low and simmer for 3-4 minutes. Meanwhile stir cornstarch into remaining ¼ cup beef broth, stirring until cornstarch is dissolved. Stir cornstarch slurry into ground beef mixture. Simmer for an additional 5-8 minutes, or until sauce has thickened and sloppy joe mixture is heated through.
Taste and adjust seasonings, if needed. Serve sloppy joes on hamburger buns topped with provolone cheese.