Wash and dry zucchini; cut in half lengthwise and hollow out centers carefully, leaving shells 1/4-inch thick. Reserve pulp.
Heat olive oil in a large skillet; sauté onion, carrot and garlic in oil until limp.
Coarsely chop zucchini pulp and add to sautéed mixture; cook a few minutes.
Put vegetable mixture into a bowl.
Cook beef in the same skillet until it loses its pink color.
Add ham and vegetable mixture; mix well.
Add egg, bread crumbs, 1 Tbsp Parmesan cheese, salt and pepper to taste and oregano; mix well.
Stuff zucchini shells with meat-vegetable mixture, mounding tops.
Pour tomato sauce into the bottom of a large ovenproof dish; arrange stuffed zucchini in sauce.
Sprinke tops with remaining cheese.
Cover tightly with foil; bake in preheated 350° F oven 30 to 40 minutes, or until tender.
Uncover during last 10 minutes of baking time to brown tops.
Servings: 6