Preheat the oven to 350°F and grease a deep 9x13 baking dish.

Bring a large pot of well-salted water to a boil. Cook the spaghetti 2 minutes shy of al dente, so it is bendy but still firm in the center. Drain (do not rinse) and toss the hot noodles with the butter until every strand is coated.

Meanwhile, brown the ground beef with the diced onion in a large skillet over medium heat, breaking it up as it cooks, about 8 minutes. In the last minute, stir in the minced garlic, Italian seasoning, salt, and pepper. Drain off most of the fat.

Stir both jars of spaghetti sauce into the meat and warm through for 5 minutes. Taste and adjust the salt.

In a medium bowl, beat the egg, then stir it into the softened cream cheese until smooth. Add the cottage cheese, 1/2 cup Parmesan, minced garlic, parsley, salt, and pepper and stir until mostly combined. A few small curds are fine. The mixture should be thick and spreadable.

Spread about 1 cup of the meat sauce thinly across the bottom of the pan. Add half the buttered spaghetti in an even layer.

Spread all of the cottage cheese mixture gently over the spaghetti with the back of a spoon.

Add the remaining spaghetti, then spoon the rest of the meat sauce evenly over the top, all the way to the edges so no noodles are left exposed.

Cover tightly with foil (spritz the underside with cooking spray) and bake 30 minutes.

Uncover, scatter on the mozzarella and remaining 1/4 cup Parmesan, and bake another 15 to 20 minutes, until melted, bubbly, and golden in spots. For a blistered top, broil 1 to 2 minutes, watching closely.

Let it rest 15 minutes before cutting, so the layers set and it slices cleanly.