Preheat the oven to 400°F (200°C).
Cut the spaghetti squash in half lengthwise and scoop out the seeds.
Place the squash halves cut-side down on a baking sheet lined with parchment paper.
Roast in the oven for 30-35 minutes, or until the flesh is tender and can be shredded easily with a fork.
While the squash is roasting, heat olive oil in a large skillet over medium heat.
Add the chicken pieces and season with cumin, chili powder, smoked paprika, garlic powder, onion powder, salt, and black pepper.
Cook the chicken for 6-8 minutes, stirring occasionally, until cooked through and lightly browned.
Remove the skillet from heat and stir in the diced tomatoes, black beans, and corn.
When the spaghetti squash is done roasting, let it cool slightly.
Use a fork to shred the flesh of the squash into strands and transfer to a large mixing bowl.
Add the cooked chicken mixture to the shredded squash and stir to combine.
Add half of the cheddar and Monterey Jack cheeses and mix well.
Transfer the mixture to a 9×9-inch (23×23 cm) baking dish and spread evenly.
Sprinkle the remaining cheddar and Monterey Jack cheeses evenly on top.
Bake uncovered at 375°F (190°C) for 10-12 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let cool for 5 minutes.
Sprinkle chopped cilantro and green onions over the casserole.
Serve warm with a dollop of plain nonfat Greek yogurt on top.