To prepare lasagna, cook noodles according to package directions, omitting salt and fat. Drain and rinse under cold water. Drain.
Heat oil in a large nonstick skillet over medium-high heat. Add onion, mushrooms, spinach, and 3 garlic cloves; sauté 5 minutes or until onion and mushrooms are tender. Remove from heat, and stir in cheeses, 2 tablespoons basil, 1/2 teaspoon salt, and 1/4 teaspoon crushed red pepper.
To prepare sauce, place vinegar and remaining ingredients in a blender; process until smooth.
Place cooked noodles on flat surface; spread 1/4 cup cheese mixture over each noodle. Roll up noodles, jelly-roll fashion, starting with short side. Place the rolls, seam sides down, in a shallow 2-quart microwave-safe dish. Pour 1/4 cup sauce over each roll, and cover with heavy-duty plastic wrap. Microwave at high 5 minutes or until thoroughly heated. Sprinkle with 2 tablespoons basil.