Heat the oven to 400°. In a medium bowl, whisk together the eggs and milk. Add the sun-dried tomatoes, oregano, salt, pepper and 1/2 cup of the mozzarella and whisk until well blended. Set aside.
Heat the oil in an oven-proof 10-inch skillet over medium heat. Add the onion and cook, stirring often, until softened, about 4 minutes. Add the mushrooms and zucchini and continue cooking and stirring, until the vegetables have softened, about 7 minutes.
Spread the vegetables evenly in the bottom of the skillet. Pour the egg mixture over the vegetables and cook without stirring until the frittata begins to set on the bottom, about 3 minutes.
Scatter on the remaining cheese and the pepperoni. Place the skillet in the oven and cook until the frittata is set, about 15 minutes.
Use heat-proof spatula to loosen the frittata and slide it onto a platter. Sprinkle on the basil, slice and serve.