In a large bowl stir together mashed potatoes, cheese, flour, cilantro, and pepper. Form potato mixture into 8 patties, each about 3/4 inch thick.
In a shallow dish beat together the egg and water. In another shallow dish place bread crumbs. Dip potato patties in egg mixture, then in bread crumbs, turning to coat both sides.
In a large nonstick skillet heat 1 teaspoon of the oil over medium heat; reduce heat to medium-low. Add 4 patties to skillet; cook for 4 minutes or until bottoms are golden brown. Gently turn patties and cook 4 to 5 minutes more, or until golden brown. Remove to baking sheet. Keep warm in 300 degree F oven. Cook remaining patties, using remaining 1 teaspoon oil.
Meanwhile, in a small bowl stir together sour cream and tapenade. Serve patties hot with sour cream mixture. Makes 8 servings.