This meal has all the fun and flavor of traditional spaghetti and meatballs, but without the carbs and high calories.
Preheat oven to 375 degrees. Season cut sides of squash with 1/4 teaspoon salt. Bake, cut sides down, on a baking sheet until tender, about 45 minutes. Let stand until cool enough to handle. Scrape flesh into strands using a fork. Let drain, covered to keep warm, in a colander set over a bowl.
Meanwhile, heat 1 teaspoon oil in a medium skillet over medium heat. Cook onion and garlic, stirring, until soft but not brown, 8 to 10 minutes. Add oregano; cook until fragrant, about 30 seconds. Divide mixture between 2 bowls.
Stir 1 tablespoon plus 1 1/2 teaspoons cheese into 1 bowl of onion-garlic mixture. Mix in breadcrumbs, turkey, 1/2 teaspoon salt, and 1/4 teaspoon pepper using your hands. Form mixture into 12 balls.
Heat 2 teaspoons oil in a large skillet over medium heat. Brown meatballs, turning, 4 to 6 minutes; transfer to a plate. Add remaining teaspoon oil to skillet. Cook mushrooms, 1/4 teaspoon salt, and 1/8 teaspoon pepper, adding a few tablespoons water if skillet browns too quickly, until soft and beginning to brown, 6 to 8 minutes. Add remaining bowl of onion-garlic mixture, meatballs, and stock; bring to gentle simmer. Cook, partially covered, until meatballs are cooked through, 4 to 5 minutes. Add spinach; cook until just wilted, about 1 minute.
Divide squash and meatball mixture into 4 servings. Sprinkle with remaining cheese.