Preheat the oven at 350 F and brush the cut sides of each squash using olive oil; season with salt and pepper.
Place cut sides of squash down on two baking sheets. Roast 25 minutes or until tender.
Melt butter and olive oil in a skillet. Add celery with leeks, salt and pepper, cooking on medium heat for about eight minutes, stirring now and then.
Add apples and thyme, cooking on medium high about five minutes, or until until the apples begin to soften.
Scrape the mixture into a bowl. Work in bread, parsley, stock, chestnuts, and cream, tossing to mix well; salt and pepper.
Turn the squash so cut sides face up. Fill the cavities with stuffing and bake 20 minutes, or until tender and golden brown.