Prepare a square baking (or appropriate-sized) dish by spraying with oil or non-stick cooking spray. Preheat oven to 400 degrees.
Cut off top of 6 peppers to fully remove stem and center rib. Scoop out any remaining ribs and seeds. Remove stem, ribs, and seeds from remaining pepper and chop.
Combine beef, onion and the 1 chopped pepper in a frying pan and saute over medium high heat until beef is no longer pink. If needed, drain excess fat from beef and return mixture to pan.
Add 3 tablespoons of tomato paste to beef mixture and saute for 2 to 3 minutes. Stir in rice, zucchini and can of diced tomatoes, undrained. Add salt to taste (I used about 1/2 teaspoon.) Reduce heat to medium and cook for 5 minutes, stirring often.
Arrange hollowed peppers in baking dish so that they stand upright. It helps if the dish is just big enough to accomodate the peppers so that they help each other stand up. If necessary, trim bottoms of peppers with knife to create a flat surface. Generally fill each pepper with meat and vegetable mixture.
Mix remaining tomato paste with about 1/3 cup of water and stir to consistency of tomato soup. Pour over stuffed peppers. If needed, add more water to bottom of pan so that peppers are sitting in about a quarter inch of water. Top each pepper with 1 tablespoon of shredded cheese.
Very loosely tent pan with foil and bake for 30 minutes. Remove foil and bake another 5 minutes.