Preparation

• 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.