Heat 1 tablespoon olive oil and butter in a large pot over medium heat. Add onions and garlic; cook and stir until onions are almost translucent, about 4 minutes. Add beef shanks, short ribs, and salt; cook and stir until beef shanks and short ribs are no longer red, about 5 minutes.
Pour water into the pot; stir in peppercorns and bay leaves. Simmer until beef is tender, 45 minutes to 1 hour. Discard bay leaves. Add tomato sauce, Cheddar cheese, liver spread, and bread crumbs. Simmer until flavors combine, about 10 minutes. Stir in chile peppers.
Heat remaining 2 tablespoons olive oil in a skillet over medium heat. Add potatoes and carrot; cook and stir until golden brown and tender, about 10 minutes. Stir into the pot. Serve stew with green bell pepper and red bell pepper.
