Preheat the oven to 375 degrees and bring a large pot of salted water to a boil. Cook the rigatoni until just al dente, then drain and set aside.
In a mixing bowl, combine the ground beef, breadcrumbs, egg, salt, and black pepper. Mix until evenly blended, then shape the mixture into 12 to 16 small meatballs.
Heat the olive oil in a large skillet over medium heat. Add the meatballs and cook, turning occasionally, until browned on all sides, about 6 to 8 minutes. They do not need to be fully cooked through at this stage.
Spread 1 cup of marinara sauce in the bottom of a 9-by-13-inch baking dish. Add the drained rigatoni and remaining marinara sauce, then gently toss to coat the pasta.
Nestle the browned meatballs into the pasta mixture. Sprinkle the shredded mozzarella and grated Parmesan evenly over the top.
Bake uncovered for 20 to 25 minutes, until the cheese is melted and beginning to brown at the edges. Let the dish rest for 5 minutes before serving.