Preheat the oven to 375°F.
Carefully, using a sharp knife, cut the spaghetti squash in half lengthwise (from the stem to the bottom). Don't cut through the stem; cut to one side of the stem. Scoop out the seeds and discard.
Brush the flesh of each half of the spaghetti squash with ½ tablespoon of the olive oil and season with salt and pepper.
Place the spaghetti squash, cut-side down, on a baking sheet lined with aluminum foil (for easy clean-up).
Bake for 45 minutes or until tender and you can easily pierce it with a knife.
Remove the spaghetti squash from the oven, carefully turn it over, and allow it to cool for a few minutes until it is not too hot to handle.
While the spaghetti squash is roasting and cooling, make the Buffalo sauce and the filling.
In a small saucepan, combine the butter, tomato sauce, and cayenne pepper sauce. Cook over low heat, stirring occasionally, until the butter is melted and the sauce is heated through. Remove from the heat and set aside.
In a large skillet, heat 1 tablespoon of olive oil over medium-high heat. Add the carrots, celery, and onion; sauté, stirring frequently, just until they begin to soften.
Add the chicken to the pan; season with salt and pepper. Cook, stirring frequently, just until the chicken is cooked through and no longer pink.
Add half of the Buffalo sauce (about 1 cup); stir to combine. Taste and adjust seasoning if needed.
Using a fork, gently scrape the flesh of the squash into spaghetti-like strands. Leave the squash in the shells.
Divide the chicken mixture evenly between the two squash halves.
Top each squash half with ½ cup mozzarella cheese.
Bake for 15 to 20 minutes or until heated through and the cheese is melted.
Drizzle with additional Buffalo sauce, ranch dressing, and sprinkle with green onions.