Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until cooked through but firm to the bite, about 7 minutes. Drain and toss in a bowl with olive oil; refrigerate until cooled, about 15 minutes.
Preheat oven to 375 degrees F (190 degrees C). Spray 12 muffin cups with cooking spray.
Toss cooled spaghetti with 1 cup Parmesan cheese. Divide spaghetti between the 12 prepared muffin cups, arranging noodles in each cup to create "nests" for the meatballs.
Top each "nest" with 1 tablespoon pasta sauce, 1 meatball, and 1 more tablespoon pasta sauce, respectively. Sprinkle remaining Parmesan cheese over the tops of each meatball "nest."
Bake in the preheated oven until pasta and meatballs are heated through and cheese melts, 20 to 25 minutes. Cool slightly before transferring muffin bites to a serving platter.