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 and 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 with minced basil.