Duck populations on Long Island have diminished over the years. The one remaining duck farm on the North Fork, Crescent, in Aquebogue, provided the birds for David Page and Barbara Shinn's wedding lunch.
In a large bowl, combine the oil, shallots, thyme and a generous grinding of pepper. Add the duck breasts and marinate for 1 hour.
Light a charcoal grill. Season the duck breasts with salt and grill over a medium-hot fire for 3 to 4 minutes per side for medium rare. Slice the duck crosswise at an angle and fan the slices on plates. Serve with the Apricot Mustard.