Prepare the grill for direct cooking over medium heat (350° to 450°F).
In a medium bowl combine the oil, salt, and pepper. Add the potato wedges to the bowl and toss to coat evenly.
Brush the cooking grates clean. Grill the potatoes over direct medium heat, with the lid closed as much as possible, until they are golden brown and quite tender, 8 to 10 minutes, turning occasionally. Transfer the potatoes back to the medium bowl.
In a small bowl mix the butter and mustard. Drizzle over the potatoes. Add the herbs and stir to coat the potatoes evenly. Serve warm.