Place a 1-quart saucepan over medium-high heat and add 1 tablespoon of butter to the pan. When the butter melts, add the shallots to the pan and saute until softened, about 1 minute. Sprinkle the flour over the shallots, and stir to combine. Add the garlic to the pan and cook for 30 seconds. Deglaze the pan with the cider vinegar and cook until the vinegar is nearly reduced, about 1 minute. Add the cider and the applesauce to the pan and cook until the liquid is reduced by half, about 5 minutes. Add the chicken stock and thyme to the pan, bring to a boil, and reduce to a simmer. Cook until the sauce is slightly reduced and thick enough to coat the back of a spoon, about 5 minutes. Season the sauce with salt and pepper, and quickly stir in the remaining tablespoon of butter. Serve the sauce spooned over the pork loin.
Yield: 1 1/2 cups