Preheat the oven to 400°F/200°C, then cut each acorn squash in half and scoop out the seeds with the help of a spoon or an ice cream scoop and discard the seeds.
Place on a sheet pan, drizzle with olive oil, season with salt and pepper and roast for 30-40 minutes or until fork tender.
Meanwhile, make the filling: In a skillet over medium high heat, add olive oil and melt the butter then add ground chicken. Cook until it’s browned.
Add the mushrooms, onion, celery and apple and cook for 4-5 more minutes or until the onions are soft and translucent. Add garlic, thyme, salt, pepper and cook for 30 seconds.
Mix in the parmesan and remove from heat.
When the acorn squash are cool enough to handle, carefully scoop out the flesh leaving about ¼ inch of wall all around the squash (try not to create a hole in of the sides, I use an ice cream scoop to do this, or a spoon).
Add the scooped squash to the filling, and stir to combine.
Divide the filling between the 4 acorn squash halves
Top the filling with shredded cheese and roast for 5 minutes, then broil for a couple of extra minutes until the top is bubbling and lightly browned.