Grilled Potatoes with Garlic Aioli

In a large saucepan, cover the potatoes with cold water and bring to a boil. Cook over moderate heat until tender, 30 minutes. Drain and let cool for 20 minutes. Cut the potatoes in half.

Meanwhile, in a food processor, process the mayonnaise, lemon juice, garlic and mustard. With the machine on, add 1/2 cup of the olive oil and the vegetable oil in a thin stream and blend until emulsified. Season with salt and pepper and refrigerate until chilled.

Light a grill. Toss the potatoes with the thyme and the remaining 1/4 cup of olive oil and season with salt and pepper. Grill over a hot fire for about 10 minutes, turning occasionally, until browned and sizzling. Transfer the potatoes to a platter and serve with the aioli.