Preheat your oven to 400°F (200°C) while you prepare your squash and filling.
Cut both ends of the acorn squash flat for stability, then slice it vertically in half. Scoop out all seeds using a spoon.
Brush the insides of each half with olive oil, then season with garlic salt and pepper before placing them cut-side down on a baking sheet. Roast in the preheated oven for about 50 minutes until tender.
While the squash is roasting, heat another tablespoon of olive oil in a skillet over medium heat. Add ground turkey seasoned with salt and pepper, cooking until browned and fully cooked through.
Remove cooked turkey from the skillet, then add more olive oil if needed along with onions and thyme, cooking until onions are translucent—about 5 minutes. Stir in celery, apple, cranberries, chicken stock, salt, pepper, breadcrumbs, and cheese until combined.
After removing the roasted squash from the oven, fill each half generously with turkey mixture before returning them to bake for an additional 15 minutes until everything is heated through and golden on top.