Season the chops with salt, pepper and cayenne. In a skillet heat the oil over moderately high heat until almost smoking. Cook the pork chops until well browned on either side, about 2 to 3 minutes per side. Remove chops to a plate, cover with foil and keep warm. Deglaze the skillet with 2/3 cup pineapple juice, stirring to remove browned bits from bottom of pan. Stir in 1 tablespoon of the minced gingerroot and the brown sugar and bring sauce to a simmer. Return the chops and any juices that have collected to the skillet, reduce heat and simmer, covered, for 6 to 8 minutes until meat is cooked through. Remove chops to a plate, cover with foil and keep warm. If necessary simmer sauce until slightly reduced. Mix together the cornstarch and cold water and stir into the simmering sauce, continuing to stir until thickened. Reduce heat, stir in mustard and adjust seasoning with salt and pepper.
In a bowl combine pineapple, watermelon, the remaining tablespoon of gingerroot, scallions, jalapeno, parsley, lime juice and the remaining 1/3 cup pineapple juice, mixing well.
Serve the chops warm, glazed with the sauce and garnished with the pineapple & watermelon relish.