Preheat the oven to 350 degrees and butter the bottom of a 9- by 13-inch glass baking dish. Cook the lasagna noodles according to the package directions. If not using them immediately, lay them out on a piece of parchment paper or nonstick foil so they don’t stick together.
While the pasta cooks, combine the spinach, ricotta, Parmesan, egg, garlic, nutmeg, salt, and pepper in a medium bowl.
Spread about 2 tablespoons of the spinach mixture over each noodle. Starting with a short side, roll up jellyroll style and place the rolls seam side down without touching in the prepared baking dish. You should be able to fit about 16 rolls in your dish (you might have a few noodles leftover).
Make the topping by melting the butter and then stirring in the salt, ground red pepper, and parsley. Spoon this mixture over the tops of the pasta rolls. Sprinkle with ¼ cup Parmesan. Cover the dish tightly with aluminum foil and bake 35 minutes, until piping hot all the way through (the centers should read 160 degrees on an instant-read thermometer). Let rest a few minutes before serving.