Heat a covered grill to medium, about 400°F, with a cooler area available. Cut 4 large double-layer sheets of heavy-duty foil.
Toss potato slices with melted butter, buttermilk powder, chives, dill, garlic powder, onion powder, salt and pepper until evenly coated. Divide among the foil sheets in shallow overlapping layers.
Add 1 tablespoon water to each packet and fold the edges tightly to seal, leaving a little headroom for steam. Grill covered for 25 to 30 minutes, turning packets once halfway through.
Move packets to the cooler side, open one carefully away from your face and test a potato slice with a fork. Reseal and cook a little longer if it is still firm.
Open all packets, divide cheddar over the potatoes and close the grill lid for 3 to 5 minutes until the cheese melts. Rest for 3 minutes and serve one packet per person.