Preheat the oven to 350°F (175°C).
In a large nonstick skillet over medium-high heat, cook the ground beef or turkey, stirring and breaking up with a spoon, until browned and cooked through; drain any excess fat.
Add the marinara sauce to the skillet with the meat, bring to a boil, then reduce heat and simmer 5 minutes.
Meanwhile, in a bowl combine the fat-free cottage cheese and grated Parmesan until smooth.
Lightly coat a 13x9 inch baking dish with cooking spray. Spread 1/2 cup of the meat sauce over the bottom of the dish.
Arrange 4 no-boil lasagna noodles over the sauce. Spread half of the cottage cheese mixture over the noodles, then spoon 1 cup of the meat sauce over the cheese and sprinkle with 1/3 cup of the shredded cheddar.
Repeat the layers: 4 noodles, remaining cottage cheese mixture, 1 cup meat sauce, and 1/3 cup cheddar. Top with remaining noodles and spread the remaining meat sauce over them.
Cover the dish and bake for 30 to 35 minutes, until the noodles are tender.
Uncover, sprinkle with the remaining 1/3 cup cheddar (or mozzarella), and bake an additional 5 minutes, until the cheese melts.
Let the lasagna stand 10 minutes before cutting into 9 servings and garnish with chopped parsley if desired.