Melt the butter in a saute pan over medium heat. Whisk the flour into the butter until the flour has dissolved, making a roux. Let cook 2 to 3 minutes, and then reduce the heat to medium-low.
In a liquid measuring cup, combine the cider and broth together. Slowly pour in over the roux and whisk constantly until all liquid has been incorporated into the mixture. Stir in the mustard. (If there are any pan drippings from the roasted turkey you can add them at this point). Add fresh thyme and let simmer until the gravy is thickened, 4 to 5 minutes.