Prepare a grill for medium heat (350° to 450°). In a large bowl, toss potatoes with oil, kosher salt, and pepper.
Set out 4 sheets heavy-duty foil (each about 12 by 26 in.). Oil foil; divide potatoes among sheets, arranging them cut side down in a single layer on the short half of each sheet. Fold other half of each sheet over potatoes and crimp edges to seal.
Grill packets, crimped sides up, covered, rotating halfway through, until potatoes are tender when pierced through foil, 20 minutes. Open packets; if potatoes aren't brown on cut sides, cook longer.
Transfer potatoes to a large bowl. Toss with butter and dill. Arrange on a platter; sprinkle with coarse sea salt if you like.
Make ahead: Up to 3 days ahead, grill potatoes, remove from foil, and chill. Reheat in an oiled baking pan in a 450° oven until hot, 15 minutes, then proceed with step
Great flavor. I used a squeeze tube of dill which had a little stronger flavor than the dried. I would do it that way again. Also didn't oil the foil (purely from a concern about calories) so the potatoes stuck a little to the foil, but they were easy to pry off. Yum! We will make these again. Wonderful with burgers.
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