Preheat oven to 350°F and lightly spray a 12-cup muffin pan with cooking spray.
Cook the spaghetti according to package directions until al dente, then drain and return to a large bowl.
Toss the hot spaghetti with the melted butter, then add the whisked eggs and 1/2 cup grated Parmesan; mix until the pasta is evenly coated.
Divide the spaghetti evenly among the 12 muffin cups, pressing the pasta down and up the sides to form small nests.
While the pasta cooks, brown the Italian sausage in a skillet over medium heat, drain any excess fat, then stir in the spaghetti sauce and remove from heat.
In a small bowl, combine the cottage cheese, 1/4 cup Parmesan, and dried parsley; spoon or divide this mixture evenly into each spaghetti cup.
Spoon the sausage and sauce mixture over each cottage-cheese–topped spaghetti cup; you may have leftover sauce.
Top each cup with shredded mozzarella cheese.
Bake for 30 minutes until the cheese is lightly browned and the pies are set; let cool a few minutes before removing from the pan.
