Using a large, sharp knife, pierce a spaghetti squash in several places. Place the spaghetti squash in a glass baking dish and cook in the microwave on HIGH for 12 to 15 minutes, turning the squash halfway through cooking.
Before handling let the squash stand for 10 minutes. Cut in half lengthwise and scrape out the seeds and fibers.
Using a fork, twist out strands of the spaghetti squash flesh and place in a large bowl. Let stand at room temperature. Save the shells of the squash for stuffing later.
Preheat the broiler.
Heat the olive oil in a large nonstick skillet set over medium-high heat. Add the ground turkey and onion. Cook, breaking up the turkey with a wooden spoon, until the turkey is cooked through and the onions are tender.
Stir in the garlic, cumin, oregano, chili powder, paprika, salt and pepper, and cook for 1 minute.
Stir in the diced tomatoes and spaghetti squash strands, and cook until heated through, about 1 minute.
Place the spaghetti squash shells on a large baking sheet and fill with the turkey mixture. Top each with 2 tablespoons grated cheese.
Place under the broiler and cook until the cheese is melted, about 1 minute. Watch closely so it doesn’t burn.