Preheat the oven to 350°F (175°C). Butter a 10 x 14-inch baking pan or two pie pans.
Cook the spaghetti according to package directions until al dente; do not rinse. Drain and return to the pot or place in a large bowl.
Add the butter, grated Parmesan, and eggs to the hot cooked spaghetti and toss well until the butter melts and the mixture is evenly combined.
Transfer the spaghetti mixture to the prepared pan(s), spreading it evenly. If using two pie pans, divide evenly.
Pour the spaghetti sauce over the top, spreading it gently, then spoon the cottage cheese over the sauce in an even layer.
Sprinkle additional grated Parmesan over the cottage cheese.
Bake in the preheated oven for 30 minutes.
Remove the pie from the oven, sprinkle the shredded mozzarella evenly on top, and return to the oven for an additional 10 minutes, until the cheese is melted and bubbly.
Let rest a few minutes before slicing and serving.