Preheat oven to 400 degrees. Bring a large pot of water to boil. Generously salt water; add noodles and cook according to package directions. Drain, and rinse with cold water. Lay noodles on a baking sheet, separating layers with parchment or waxed paper.
In a medium bowl, combine ricotta, parsley, and egg. Season with 1 1/2 teaspoons salt and 1/4 teaspoon pepper.
Lightly coat a 9-by-13-inch baking dish with olive oil. Begin layering: Place 4 noodles in dish, slightly overlapping. Top with half the meat sauce and 4 more noodles. Top with half the ricotta filling, then half the mozzarella. Repeat the layering process, ending with the mozzarella. Sprinkle top with Parmesan.
Cover with lightly oiled foil. Place on a rimmed baking sheet; bake for 30 minutes. Uncover, and bake until bubbling and browned, 30 to 40 minutes more. Let cool 10 minutes before serving.