Get a skillet very hot. Once it is hot, add oil to it and brown the chicken on both sides. Cook for about 5 minutes on each side, until it's a nice, golden color. Remove from the pan and set aside on a plate. It's okay that it's undercooked, it will finished cooking in the sauce.
Over high heat, brown the shallots.
Add cider vinegar and scrape the bottom of the pan, getting all the shallots and any leftover browned chicken bits.
Before the vinegar evaporates, add the cider and the apple slices. Let this reduce on high for about 3 minutes. The apples and shallots will get very tender.
While they reduce, mix the chicken broth and the cornstarch until there are no lumps left, then slowly add it to the bubbling cider and apples, stirring all the time while the sauce thickens.
Mix in thyme, mustard, salt and pepper.
Return the chicken and its juices back into the sauce, turn down to medium-low and summer for at least 10 minutes, or until the chicken is cooked all the way through. Serve with hot cooked rice.