Sprinkle the chicken pieces with salt and pepper. Heat 2 Tbsp of the oil in a large frying pan set over medium-high heat. Working in batches, brown the chicken pieces, flipping once, until browned on both sides, 8-10 minutes per batch. If the bottom of the pan begins to look dry, add a little more oil.

Transfer the browned chicken pieces to a large baking dish and top with the apple wedges and thyme sprigs.

Preheat oven to 375°F.

Lower the heat under the frying pan to medium and add the shallots. Season with a little salt cook, stirring occasionally, until softened and lightly browned, about 5 minutes. Add the chopped thyme and cook for 1 minute, then stir in the apple cider and the cider vinegar, scraping up any browned bits at the bottom of the pan. Raise heat to high, and cook until the liquid has reduced by half, 4-5 minutes.

Stir in the broth and bring to a boil, then carefully pour the braising liquid over the chicken and apples. Cover the baking dish with foil and braise in the oven until the chicken is very tender, 45-55 minutes.

Remove baking dish from the oven and transfer the chicken and apples to a serving platter.

Transfer 1½ cups (360 ml) of the braising liquid to a medium saucepan set over high heat. Bring to a boil and cook, stirring often, until the liquid reduces by two-thirds, 10-15 minutes. Spoon the sauce over the chicken and serve warm.