Bring a medium pot of salted water to a boil. Place potatoes in the boiling water, reduce heat and simmer until fork-tender, 10-15 minutes. Drain, then let cool slightly
Meanwhile, mix vinegar, whole grain mustard, mayo in a large bowl.
Cut larger potatoes in quarters and smaller potatoes in half and transfer to bowl with vinegar mixture; toss to coat. Let cool. Cut mustard greens into thin strips, then add to potatoes and toss again.
Heat a large skillet with drizzle of oil. Add brats to the hot skillet and sear cooked through until browned on all sides, about 15 minutes. Serve brats with potato salad and a sharp mustard.