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Melt butter in a medium-sized Dutch oven. When the bubbles subside, add the red onions and saute until translucent and tender, about 3 to 5 minutes. Add the shredded cabbage and apples and cook over medium heat for another 8 to 10 minutes. Add the chicken stock, apple cider, red wine vinegar, and brown sugar. Place all of the spices on a piece of cheesecloth and tie the ends together to make a bundle. Add the spice bundle, 1 teaspoon of the salt, and 1 teaspoon of the pepper to the pot and stir to combine. Bring the liquid to a boil, reduce heat to medium low, cover the Dutch oven with a lid or aluminum foil and cook, stirring occasionally, until just tender, 20 to 25 minutes.
Rub the pork loin with the mustard and chopped herbs; season with the remaining salt and pepper. Roast in the oven until a thermometer inserted into the thickest part of the roast registers 140 to 145 degrees F on an instant-read thermometer, usually 35 to 40 minutes. Allow the roast to rest for 10 minutes before slicing.
Slice the roast crosswise against the grain into thin slices and serve with the red cabbage.