Preheat the oven to 400°F (200°C).
Carefully trim a small amount from the top and bottom of the acorn squash to create stable surfaces. Cut the squash in half vertically and scoop out the seeds and stringy center with a spoon.
Brush the cut sides of the squash with some of the olive oil. Season with garlic salt and black pepper.
Arrange the squash halves on a baking sheet or in a baking dish. Roast for 50–60 minutes, or until the flesh is tender when pierced with a fork.
While the squash roasts, heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the ground turkey, season with salt and pepper, and cook until browned and completely cooked through. Break the meat into small pieces as it cooks.
Transfer the cooked turkey to a plate and set aside.
Add a little more olive oil to the same skillet. Add the chopped onion and dried thyme. Cook for about 5 minutes, until the onion becomes soft and translucent.
Add the celery, chopped apple, and dried cranberries. Cook for another 3–4 minutes, stirring occasionally.
Return the turkey to the skillet. Pour in the chicken stock, season with salt and pepper, and cook for approximately 3 minutes so the flavors can combine.
Stir in the breadcrumbs and Parmesan until evenly incorporated. Taste and adjust the seasoning if necessary.
Divide the filling generously between the roasted squash halves. Return the Turkey Stuffed Acorn Squash to the oven and bake for another 15 minutes.
Let the stuffed squash cool for a few minutes before serving.