1. Soak 8 wooden skewers in water 30 minutes. (Omit if using metal skewers.)
2. Meanwhile, bring potatoes and water to cover to a boil in a Dutch oven over medium-high heat; cook 10 minutes or just until crisp-tender. Drain.
3. Combine steak and 1/2 cup vinaigrette in a large zip-top plastic freezer bag. Thread 8 potato halves onto 1 double set of skewers (2 skewers side-by-side), leaving a 1/8-inch space between pieces; repeat with 3 double sets of skewers and remaining potatoes. Cut 4 to 8 crosswise slits 1/4 inch deep on top of each potato. Combine potatoes and 1/2 cup vinaigrette in another large zip-top plastic freezer bag. Seal bags, and chill 3 hours, turning occasionally.
4. Meanwhile, soak remaining 6 wooden skewers in water 30 minutes. (Omit if using metal skewers.)
5. Preheat grill to 350° to 400° (medium-high) heat. Remove steak and potatoes from marinades, discarding marinades. Thread steak onto 6 skewers, leaving a 1/8-inch space between pieces. Sprinkle with desired amount of salt and pepper.
6. Grill potatoes and steak at the same time, covered with grill lid, 6 to 7 minutes on each side or until steak reaches desired degree of doneness and potatoes are golden brown, basting potatoes and steak with melted butter with each turn.
7. Toss together arugula, next 5 ingredients, and 2 Tbsp. vinaigrette. Serve kabobs with arugula salad and remaining vinaigrette.