In a large pot over high heat, place the potatoes with water to cover and bring to a boil. Let boil for about 20 minutes, or until potatoes are tender. Drain and transfer potatoes to a large bowl. Add the milk, mozzarella cheese and 2 tablespoons of the Parmesan cheese.
Using an electric mixer, beat the potatoes until almost smooth. Then beat in the eggs, drain the tuna and stir the tuna into the potato mixture. Then stir in the green onion, and season with salt and pepper to taste.
Transfer mixture to a lightly-greased 10-inch diameter glass pie dish and top with the remaining Parmesan cheese.
Bake at 400 degrees F (200 degrees C) for 45 minutes, or until golden brown.