Slice the spaghetti squash in half lengthwise and scoop out the seeds in the center. Add enough water to cover the bottom of a baking dish large enough to hold both halves of the squash, and place the squash in the pan, cut side down. Roast for 30 to 40 minutes, or just until tender enough to be pierced with the tines of a fork. Take care not to overcook.
While the squash is roasting, brown the ground beef in a large, heavy skillet over medium-high heat, breaking it up with a wooden spoon as it cooks. While it is still somewhat pink, add the onion and continue cooking until the meat is cooked through and the onion is soft and translucent.
Reduce the heat to medium and stir in the tomato paste, water, spices and salt and pepper. Simmer uncovered and stirring occasionally, until the chili is thickened, about 20 minutes.
Once the squash is roasted, scrape out the flesh with a fork to make long strands into a bowl, handling the hot squash with care. Toss the spaghetti squash with the ghee and Parmesan and divide between 8 plates. Top with the chili, cheese and onion and serve.