Preheat the oven to 400 degrees F. Butter a 13- by 9- by 2-inch baking dish. Set aside.
For the potatoes: In a large saucepan, combine the butter, salt and potatoes. Add enough cold water to cover the potatoes by 1 inch. Bring to a boil over medium-high heat. Boil until the potatoes are very tender, about 15 minutes. Drain the potatoes and return them to the same pot. Using a potato masher, mash the potatoes until smooth. Mix in the mozzarella, milk, Parmesan and butter. Season with salt and pepper. Transfer the potatoes to the prepared baking dish.
For the peas: In a medium skillet, melt the butter over medium heat. Add the thawed peas and cook until heated through. Add the salt and pepper.
Using a large spoon, make a 4-inch well in the center of the potatoes and fill with the cooked peas.
For the topping: Stir the cheese and breadcrumbs in a small bowl to blend. Sprinkle the breadcrumb mixture over the mashed potatoes (can be prepared up to this point 6 hours ahead of time; cover and chill).
Drizzle the top with olive oil and bake until the topping is golden brown, about 20 minutes.