Preheat oven to 400°F. Wash the outside of the squash and cut each in half. Use a spoon to remove seeds and stringy flesh, leaving a smooth cavity for the filling.
Place squash halves on a baking sheet, flesh side up. Brush all over with a thin layer of oil and sprinkle with salt and pepper to taste. Roast until tender, 35-40 minutes.
While squash is roasting, make the filling. Combine farro, vegetable stock and the sprig of thyme in a medium saucepan and bring to a simmer, cooking until liquid is evaporated and farro is tender, 25 to 30 minutes. Stir occasionally. When done, remove the thyme sprig.
Heat 1 Tbsp. oil in a large skillet over medium heat. Sauté onion, celery, apples and mushrooms until softened, about 10 minutes. Add garlic, thyme, and salt and pepper to taste and cook for about a minute, until fragrant.
Add kale and cook, stirring frequently, until kale is tender. Toward the end of cooking, add the apple cider vinegar. Stir in cooked farro.
Divide mixture among the 4 squash halves. Switch oven to broil and broil until tops are golden and filling is warmed, 2 to 3 minutes. Sprinkle with pepitas and serve.