Peel and halve peaches. Toss together peach halves, shallot, and olive oil. Grill peach halves and shallots over 400° to 500° (high) heat, covered with grill lid, 4 minutes on each side. Remove from grill; cool 10 minutes. Coarsely chop peaches and shallot. Combine with sugar, vinegar, ginger, salt, and dried crushed red pepper.