Place the potatoes in a large pot or Dutch oven and cover by 1 inch with cold water. Bring to a boil over high heat, then reduce to a simmer. Cook just until fork tender, 15 to 20 minutes. Drain and transfer to a plate to cool to room temperature.
Preheat a grill to medium-high heat (400 to 450°). Soak 10- to 12-inch wooden skewers in water.
Meanwhile, combine the butter and garlic in a microwave safe bowl. Cook, covered, on high just until melted, 30 to 60 seconds.
Place 3 to 4 potatoes on each skewer. Brush all over with the butter mixture. Place the skewers over direct heat on the grill, and cook until golden and a little charred, 6 to 8 minutes per side.
Transfer to a serving platter. Brush with any remaining garlic butter, then sprinkle with parmesan cheese and fresh herbs.
