Bring a large pot of salted water to a boil. Drop in the noodles and cook them according to the package instructions for al dente, typically about 8 minutes. Drain the noodles in a colander and transfer the cooked noodles to a baking sheet coated with cooking spray.
Once cool, move the noodles to a cutting board and cut them into chips. To do this, cut a noodle in half shortways to make 2 pieces. Cut each of the 2 pieces in half shortways again to create 4 rectangles. Cut each rectangle diagonally to create 8 triangles. Repeat with the remaining noodles.
Place the noodle pieces in a bowl and toss with the Parmesan, olive oil and oregano.
Arrange the noodles on 2 baking sheets coated with cooking spray, making sure the noodles are in a single layer and not touching one another. Bake until crisp and golden, 18 to 20 minutes. Set aside.
For the dip: Raise the temperature of the oven to 425 degrees F.
In a skillet over medium-high heat, cook the beef and sausage until browned, about 4 minutes. Add the tomatoes, tomato paste and garlic to the skillet. Season with salt and pepper. Bring to a simmer. Lower the heat and cook on low for 15 minutes to let the flavors meld and the sauce reduce slightly.
Meanwhile, mix the cottage cheese, ricotta, Parmesan and all but a pinch each of the basil and parsley in a medium bowl. Set the remaining herbs aside for garnishing the dip.
Spread half of the meat and sauce over the bottom of a 2-quart casserole dish. Using a spoon, dollop half of the cottage cheese mixture over the sauce. Sprinkle with half of the mozzarella. Repeat with the remaining meat and sauce, cottage cheese mixture and mozzarella.
Bake until the mozzarella is fully melted and the dip is bubbly, 15 to 17 minutes. Serve hot in the casserole dish with the lasagna chips on the side. Garnish with the remaining basil and parsley.