1Preheat your grill. If using a gas grill, heat it to its medium setting.
2In a medium bowl, combine the radish slices, olive oil, white wine vinegar, garlic and salt and pepper. Toss to combine.
3Lay out a large sheet of aluminum foil (roughly 18-24 inches long). Pile the radish mixture in the center and top with the sprigs of dill.
4Fold the sides of the aluminum foil in to form a sealed packet. Place the packet on the grill, seam-side up and let cook for 20-30 minutes.
5Remove the packet from the grill and let rest for 5 minutes. Carefully open the packet, being careful of escaping steam. Transfer radishes to a serving dish.
6Serve immediately. Leftovers can be chilled and eaten cold as well.