Combine tomatoes, basil, garlic, and salt in a saucepan and simmer over medium heat for about 30 minutes, until the sauce starts to thicken.
Preheat oven to 350°F.
While the tomato sauce is simmering, cook the beef and Italian frying pepper over medium-high heat in a skillet until the beef is browned.
Butter a 9" glass baking dish. Arrange a layer of potato slices on the bottom of the pan. Cover with about 1/2 of the meat, and then 1/2 of the tomato sauce. Follow this with another layer of potatoes, the rest of the meat, and the rest of the sauce. Cover this with a layer of zucchini. Top with shredded cheese and bake for about 50 minutes, until the top is bubbling and golden brown.