Heat oil in a large non-stick skillet over medium heat. Add zucchini, red onion and red pepper. Cook, stirring often, until vegetables are slightly softened, about 7 to 8 minutes. Remove from heat, stir in dried basil, dried oregano, onion powder, garlic powder and cayenne pepper.
Generously oil a muffin pan with twelve 2-3/4-inch (7 cm) diameter cups. Line bottom and sides of muffin cups with prosciutto or ham. Divide vegetable mixture between muffin cups. Sprinkle 1 tbsp (15 mL) mozzarella cheese over vegetables.
Whisk eggs thoroughly in a 4-cup (1 L) liquid measuring cup or large bowl. Carefully pour eggs into muffin cups.
Bake in a preheated 350°F (180°C) oven until frittatas are puffed and set in centre, about 20 to 25 minutes. Remove pan from oven and let stand for a few minutes. Run knife around edge of frittatas to release.