Rub catfish with basil marinade and let stand for 1 hour in the refrigerator. While the catfish is still very cold, grill for 5 minutes on each side. Slice peaches and place on top of catfish and drizzle some of the pickling juice over the top.
Basil Marinade: Mix all ingredients and reserve in the refrigerator, covered tightly.
Pickled Peaches: Combine all ingredients and boil for 4 minutes. Remove from heat and refrigerate overnight.