Preheat oven to 400°F. Brush squash halves with olive oil, salt, and pepper; roast cut-side down 30–40 minutes until strands pull easily.
Scrape squash into a bowl, discard shells, and fluff with a fork. Lower oven to 375°F.
Mix shredded chicken, hot sauce, Greek yogurt, half the cheddar, green onions, and butter into the squash. Taste and adjust salt or heat.
Transfer to a greased 9x9 baking dish. Sprinkle with remaining cheddar, blue cheese, and panko if using.
Bake 15–20 minutes until bubbly and golden on top. Let rest 5 minutes, then serve with extra ranch or celery sticks.