On a baking sheet lined with parchment paper, brush all sides of the spaghetti squash with oil. Place each half squash cut side down.
Bake for 40-60 minutes, or until fork tender. While the squash bakes, in a large pot over medium high heat, cook the sausage and mushrooms. Let most of the water evaporate from the mushrooms.
Add the onions, garlic, and spices. Cook for 3-4 minutes or until the onion softens.
Add the sauce and simmer on medium low heat, stirring frequently until the squash is done. The sauce should thicken up a bit.
Once the squash is done, let it cool until you can handle it. Use a fork to scrape the middle of the squash so that the “spaghetti” forms.
Fold the squash, yogurt, and parmesan cheese into the meat sauce.
Lightly grease a 9 x 13 baking dish. Pour the squash mixture into the dish. Sprinkle the mozzarella cheese on top.
Bake for 15 minutes, or until the edges are bubbling and the cheese is completely melted. Let stand for 5-10 minutes before serving.