Preheat the oven to 425°F (220°C). Pour 1 1/4 cups of the marinara sauce into a 13x9x2-inch baking dish and spread to coat the bottom.
Heat the olive oil in a large skillet over medium-low heat. Add the minced garlic and sauté about 1 minute until fragrant.
Add the chopped spinach to the skillet and sauté until wilted, about 2–3 minutes. Remove from heat and let cool slightly.
In a large mixing bowl, combine the cooked spinach and garlic with the ricotta, 1 cup shredded mozzarella, cottage cheese, egg white, dried oregano, salt, and black pepper. Stir until evenly mixed.
Lay the drained lasagna noodles flat on a work surface lined with parchment paper. Divide the cheese and spinach mixture evenly, placing about 1/4 cup of filling on each noodle and spreading to cover.
Starting at the end nearest you, roll each noodle tightly and place seam-side down in the prepared baking dish, arranging them so they are close but not touching.
Pour 1 cup of marinara sauce evenly over the rolls. Sprinkle the remaining shredded mozzarella and the grated Parmesan cheese over the top.
Cover the dish with foil and bake for 20 minutes, until the cheese is hot and bubbly. Remove foil for the last few minutes if you want more browning.
Let the rolls rest a few minutes before serving. Serve with additional warmed marinara if desired.