Brush the inside of the squash halves with olive oil; season with salt and pepper. Place cut-sides up on a baking sheet.
Bake in the preheated oven until softened, about 45 minutes. Remove from oven. Cool until easily handled, 5 to 10 minutes. Scrape out strands of squash with a fork and transfer to a bowl.
Preheat oven to 350 degrees F (175 degrees C).
Mix half of the mozzarella cheese, ricotta cheese, egg, and Parmesan cheese together in a bowl. Stir into the squash. Stir in 2 or 3 tablespoons spaghetti sauce to turn mixture pink.
Spread half of the squash mixture in a 9x13-inch baking dish. Ladle half of the spaghetti sauce on top. Sprinkle with half of the remaining mozzarella cheese. Layer remaining squash mixture, spaghetti sauce, and mozzarella cheese on top.
Bake in the preheated oven until mozzarella cheese is melted and browned, 30 to 45 minutes.