Preheat the oven to 400°F (200°C).
Carefully trim a thin slice from the top and bottom of the acorn squash so it has stable, flat surfaces. Cut the squash in half vertically.
Scoop out and discard the seeds and stringy pulp.
Brush the squash halves with olive oil. Season with garlic salt and black pepper.
Place the squash cut-side up on a baking sheet and roast for 50–60 minutes, or until the flesh is tender when pierced with a fork.
While the squash roasts, heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the ground turkey and season with salt and pepper. Cook until browned and cooked through, breaking it apart as it cooks. Transfer the turkey to a plate.
Add another tablespoon of olive oil to the skillet. Add the chopped onion and thyme and cook for about 5 minutes, until the onion becomes translucent.
Add the celery, chopped apple, and dried cranberries. Cook for 3–4 minutes, stirring occasionally.
Return the cooked turkey to the skillet. Add the chicken stock and season with additional salt and pepper as needed. Simmer for about 3 minutes.
Stir in the breadcrumbs and Parmesan cheese until the mixture is well combined. Taste and adjust the seasoning.
Spoon the turkey mixture evenly into the roasted squash halves.
Return the stuffed squash to the oven and bake for 15 minutes, until the filling is hot and the Parmesan is lightly golden.