Step 1

Place the potatoes in a medium pot; add water to cover by 1 inch and 1 tablespoon of the salt. Bring to a boil over high heat; reduce the heat and simmer until the potatoes are tender when pierced with a sharp knife, about 12 minutes. Drain the potatoes; then place them back in the pan and run under cold water to cool.

Step 2

Preheat the grill to medium-high heat.

Step 3

In a large bowl, whisk together the mayonnaise, the Dijon mustard, remaining teaspoon salt, pepper, garlic and thyme.

Step 4

Drain the potatoes and slice them in half. Add to the Dijon mustard sauce and toss to coat evenly, taking care not to smash the potatoes.

Step 5

Clean and oil the grill grate. Place the potatoes on the grill and cook, covered, for about 3 minutes, or until you see nice grill marks on the first side. Using tongs, turn the potatoes and grill about 3 minutes more, until crisp and golden all over. Transfer the potatoes to a serving platter and sprinkle with chopped parsley (if using).

Step 6

Note: Potatoes can be boiled 1 day ahead of time. Bring to room temperature before grilling.