Toast the slices of whole-wheat bread. Sprinkle the tomato slices with the freshly ground black pepper. Place the tomato slices and the cucumber slices on each of two slices.
In a stainless-steel frypan, heat the olive oil over moderate heat. Crack two eggs open, inspect for any spots, and if not spotted, place in pan. When thoroughly cooked, remove and place on one of the slices of whole wheat bread. Repeat the process.
Place the cooked bull's eye eggs on each of the two slices of bread, covering the tomato and cucumber slices. Cover with the remaining slices, then cut each sandwich diagonally in half.