Halve any large potatoes to make potatoes of similar size. In a small saucepan, cook potatoes in a small amount of lightly salted boiling water for 10 to 13 minutes or just until tender. Drain well and set aside. Meanwhile, in a small bowl, combine ginger, tarragon and ⅛ teaspoon pepper; set aside.
Trim fat from chops; sprinkle with salt and ⅛ teaspoon pepper. Heat a large skillet heat oil over medium heat. Add chops and potatoes to skillet. Cook for 9 to 11 minutes or until chops are medium doneness (160°F), turning chops once halfway through cooking time and turning potatoes occasionally to brown evenly. Remove chops and potatoes from skillet; cover with foil and keep warm.
Remove skillet from heat. Drain off fat. For sauce, carefully pour wine into skillet; return to heat and stir to scrape up any browned bits. Add ginger mixture. Simmer and stir about 2 minutes or until liquid is reduced by half. Stir in mustard. Return to a simmer.
Place chops and potatoes on 2 warm serving plates and top with the sauce.