In a medium bowl, whisk together peach preserves, vinegar, sugar, oil, butter, salt and pepper. Set aside.
Heat a gas grill to mediumhigh or the coals in a charcoal grill to medium-hot.
Trim outer leaves of cabbage, keeping stem end intact. Slice lengthwise into 4 equal pieces.
Lightly grease grates. Generously brush cabbage with peach sauce. Close lid and grill for 5 to 7 minutes on uncut side. Turn and grill on cut side for 5 to 7 minutes, turning if necessary to avoid burning. Brush with additional sauce as needed.
Serve warm with any remaining sauce on the side.
