By par-cooking your potatoes before they go on the grill, they'll have a soft, almost cakey texture on the inside when they're done, but they'll still have that terrific grilled flavor. The mayonnaise not only adds flavor to the potatoes, but helps keep them from sticking to the grill.
Wash the potatoes and cut them into 3/8-inch slices. Cover the potatoes with cold water and 1 Tbs. salt in a saucepan. Bring to a boil, lower to a gentle simmer (you don't want them to break up), and cook until they're almost but not quite fully cooked, 4 to 6 minutes. The potatoes will still be a little hard in the center, but the outer edges will look opaque. Drain in a large colander and rinse with cold water until they're cool; handle them gently. Spread them out on clean dishtowels and let them sit at room temperature (for up to an hour) until you're ready to grill them.
Light a charcoal grill and allow the fire to reach a medium-hot temperature (the top of the coals should be 5 to 6 inches from the grill grate, and you'll be able to hold your hand over the fire for no more than 3 to 4 seconds when it's medium hot). Alternatively, heat the entire surface of a gas grill until it reaches medium hot.
In a medium bowl, combine the mayonnaise, mustard, rosemary, and salt and pepper to taste. Toss the potato slices with the mayonnaise mixture until the potatoes are well-coated. Put the potatoes on the grill grate in one layer, directly over the fire. Cook for 3 to 6 minutes or just until deep golden brown and crisp. With tongs, turn the pieces over to the other side. Cook until that side is deep golden brown and crisp, another 3 to 6 minutes. Remove and serve immediately.
Olive Oil & Herb-Grilled Potatoes: In place of the mustard-mayonnaise mixture, toss the potatoes with 3 Tbs. extra-virgin olive oil, 3 tsp. mixed chopped hardy herbs (such as rosemary, sage, or thyme), and a pinch of crushed red pepper flakes.
Tapenade-Grilled Potatoes: In place of the mustard-mayonnaise mixture, toss the potatoes with 3 Tbs. extra-virgin olive oil and 1 Tbs. black olive tapenade.
Photo: Scott Phillips