Heat oven to 375 degrees F. Lightly grease a baking sheet. Grease eight 1-1/2-cup individual casseroles. Bring large pot of lightly salted water to boiling over high heat.
Add potatoes to boiling water; cook 2 minutes after water returns to boiling. Add green beans and zucchini; cook 1 minute after water returns to boiling. Drain vegetables; return to pot.
Add the diced tomatoes, 2 tablespoons of the tomato paste and 1/2 teaspoon of the salt to vegetables in pot; stir to combine. Stir in the Cheddar cheese.
Mix together ground chicken, beef, egg, mushrooms, remaining 1 tablespoon tomato paste, the bread crumbs, oregano, cumin and remaining 1/2 teaspoon salt in large bowl. Divide mixture into 32 meatballs, about 2 tablespoons each. Place on prepared baking sheet.
Place about 1 cup of the vegetable mixture in each individual casserole. Place 4 meatballs on top of vegetables in each casserole. Sprinkle each with 1 tablespoon of the remaining shredded cheese and paprika.
Bake in 375 degree F oven for 30 minutes or until lightly browned and bubbly around edges. Let stand 10 minutes before serving. Makes 8 servings.