Heat a Dutch oven over medium heat. Add enough olive oil to coat the bottom.
Add the turkey legs. Let the first side brown for a couple of minutes before flipping. Continue the process until all sides are browned. Remove from the pan.
Add the onions, celery, carrots, and mushrooms. Sauté for a few minutes, stirring occasionally, until the onions are translucent.
Season with salt, pepper, and thyme.
Add the turkey legs back into the pan, along with any drippings.
Add the broth and apple cider. Cover with the lid and turn heat to low.
Let the turkey legs cook for 1 1/2 hours, or until the turkey is tender.
Preheat the oven to 350 degrees.
Nestle the sliced apples into the pot. Bake for 30 minutes uncovered.