Preheat the oven to 350 degrees F (175 degrees C). Grease a 10-inch pie plate with 1 tablespoon butter.
Bring a large pot of lightly salted water to a boil. Cook spaghetti in boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain spaghetti through a colander and return to the pot.
Stir Parmesan cheese, beaten eggs, and 2 tablespoons butter into hot spaghetti until well combined. Press mixture evenly on the bottom and up the sides of prepared pie plate to form a sturdy crust.
Heat a large skillet over medium-high heat. Cook and stir beef, onion, bell pepper, and garlic in the hot skillet until beef is crumbly and browned, 5 to 7 minutes. Drain off fat and stir in undrained tomatoes, tomato paste, sugar, and oregano. Cook, stirring occasionally, until heated through.
Spread cottage cheese over spaghetti crust, then pour in beef-tomato mixture.
Bake in the preheated oven for 20 minutes. Sprinkle mozzarella cheese over the top of pie and continue baking until cheese is melted, about 5 minutes more. Let pie stand briefly before slicing to allow layers to set.
