Pat pork dry and season well with salt and pepper. In a bowl, whisk mustard and olive oil together. Using your hands, rub mixture all over pork tenderloin. Let meat sit until it comes to room temperature, at least 20 to 30 minutes.
Place pork on a wire rack on a rimmed 36 x 18-inch baking sheet lined with foil. Place in the oven for 15 minutes. Reduce heat to 350˚F. and cook for another 10 minutes or until meat reaches an internal temperature of 145 degrees on a meat thermometer. Remove from oven, set aside, and cover with aluminum foil.
In a skillet, heat butter, vinegar, and sugar over low heat until the sugar is dissolved. Then turn up the heat to medium-high, add the cabbage and apple, and cook until the cabbage has wilted somewhat, about 10 minutes. Stir in chopped parsley.
STOP! AS CABBAGE AND APPLE COOK, WIPE DOWN BAKING SHEET, WIRE RACK, AND BOWL.
Remove foil from pork and slice.
Spread cabbage on a platter, top with pork slices, and serve.