Cut potatoes into 1/2-inch-thick slices or in half if they are small potatoes. Cook potatoes in a large pot of salted boiling water about 10-15 minutes. The potatoes will not be cooked completely through at this point. The remainder of the cooking will be done on the grill.
Meanwhile, stir together herbs, garlic, oil, salt, and pepper in a large shallow dish. Prepare a gas grill for direct-heat cooking over medium-high heat. Or, heat grill pan over medium-high heat for indoor cooking.
Drain potatoes and transfer to herb oil, tossing gently to coat.
Place potatoes on grill or in preheated grill pan on stove. Grill potatoes, covered, turning once or twice, until tender, about 5-10 minutes total. Season with additional salt to taste (I like Fleur de Sel at this point as a finishing salt).
Notes
My grocery store sells small Yukon Gold potatoes in two pound bags- they are perfect for making this dish. I cut the potatoes in half & then we get little bite sized morsels of herbed potatoes.