Return the skillet (with the reserved vegetable mixture) to medium heat. Add 1 tablespoon plus 1 teaspoon of extra-virgin olive oil. Once the oil is shimmering, carefully place the turkey meatballs in the skillet in a single layer, ensuring not to overcrowd (brown in batches if necessary). Cook for 5-7 minutes, turning them gently with tongs, until browned on all sides. Transfer the browned meatballs to a clean plate.
If the skillet seems dry, add the remaining 2 teaspoons of extra-virgin olive oil. Add the sliced mushrooms, ¼ teaspoon of coarse salt, and ¼ teaspoon of freshly ground black pepper. Cook, stirring occasionally, for 6-9 minutes, until the mushrooms are tender, have released their liquid, and are beginning to caramelize lightly. If the pan bottom becomes too brown, deglaze with a tablespoon or two of water or some of the chicken stock.
Ensure the reserved onion-pepper-garlic-oregano mixture is incorporated with the mushrooms. Return the browned turkey meatballs to the skillet. Pour in the low-sodium chicken stock and bring the entire mixture to a gentle simmer. Reduce the heat to low, partially cover the skillet, and let it simmer for 5-7 minutes, or until the meatballs are cooked through and the sauce has slightly thickened.
Stir in the fresh baby spinach (a few handfuls at a time if necessary) and cook just until it wilts into the sauce, typically 1-2 minutes.
Serve the Dish: To serve, divide the warm spaghetti squash noodles among 8 individual bowls or plates. Ladle a generous portion of the turkey meatballs and mushroom-spinach sauce over the squash. Garnish each serving with a sprinkle of the remaining 3 tablespoons of grated Parmesan cheese. Serve immediately.