Thaw tilapia, if frozen. Preheat broiler. In a medium bowl stir together vinegar, brown sugar, ginger, and salt until sugar dissolves. Reserve 1/4 cup of the mixture. Add cucumber to the remaining mixture; toss to coat. Set aside.
Rinse fish; pat dry with paper towels. Lightly coat the rack of an unheated broiler pan with cooking spray; place fish on rack of broiler pan. Brush the reserved 1/4 cup vinegar mixture over the fish. Broil 4 inches from the heat for 4 to 6 minutes or until fish begins to flake easily when tested with a fork.
Meanwhile, in a small bowl combine yogurt and the 2 tablespoons snipped mint.
Using a slotted spoon, divide cucumber slices among four plates. Top with fish and yogurt mixture. If desired, garnish with mint leaves, lemon peel, and lemon wedges and sprinkle with cracked pepper.