TOSS potatoes with oil on a large sheet of foil. Wrap tightly into a flat packet. Oil grill. Barbecue potato packet, with lid closed, until potatoes are fork-tender, about 15 min. Open foil and arrange potatoes directly on the grill. Continue grilling, with lid closed, for 5 min. Remove from grill and let cool slightly.
WHISK mayo with yogurt, Dijon, Tabasco and salt in a large bowl. Season with fresh pepper. Stir in potatoes and onion. Serve warm or at room temperature.