Heat half of a gas grill to medium-high or coals in charcoal grill to medium-hot with coals stacked to one side for indirect grilling. Lightly coat grill rack with cooking oil or cooking spray.
Cut potatoes in half lengthwise, almost all the way through so they will open like a book. Place an equal amount of onion in each and a pat of butter. Season with salt and pepper. Press closed and wrap tightly in foil. Place on the grill over direct heat. Grill with lid closed for 35 to 45 minutes.
In a medium-size bowl, stir together preserves, mustard, soy sauce and ginger. Reserve 1/4 cup for serving.
Brush turkey breast with olive oil and season with salt and pepper. Cover and grill over indirect heat for 30 minutes. Turn after 15 minutes. Brush with remaining apricot-mustard mixture and grill additional 15 to 20 minutes or until internal temperature registers 160 degrees F on an instant-read thermometer.
Serve turkey and potatoes with reserved glaze on the side.