Preheat the oven to 350°F (175°C). Spread about 1 cup of marinara sauce evenly across the bottom of a 9 x 12-inch or large oval baking dish.
Bring a large pot of salted water to a boil. Cook the lasagna noodles according to package directions until al dente, then drain in a colander and lay noodles flat on wax paper or a clean towel to dry.
In a large bowl, combine the drained cottage cheese, grated Parmesan, chopped parsley, pesto, egg, 1/2 teaspoon kosher salt, and black pepper. Stir until evenly mixed.
Measure about 1/3 cup of the cheese mixture and spread it evenly over one lasagna noodle, leaving a small border on the edges. Roll the noodle tightly and place seam-side down in the prepared baking dish. Repeat with remaining noodles and filling.
Pour the remaining marinara sauce over the rolled noodles, then sprinkle about 1 tablespoon of shredded mozzarella over each roll.
Cover the dish with foil, being careful not to press the foil onto the cheese, and bake for 40 minutes, until heated through and cheese has melted. Remove foil for the last few minutes if you prefer browned cheese.
Let the roll ups rest a few minutes, garnish with basil or parsley if desired, and serve.