To prepare the vinaigrette, combine the first 7 ingredients in a medium bowl, stirring with a whisk.
To prepare the sandwich, combine 1/4 teaspoon salt and pepper in a medium bowl. Place 2 tomato slices on each of 4 bread slices, and sprinkle evenly with half of the salt mixture. Arrange the cucumber slices over the tomato slices; sprinkle evenly with remaining salt mixture. Add arugula, onion, and chopped olives to the vinaigrette; toss to coat. Arrange the arugula mixture evenly over the cucumber slices. Top with the remaining bread slices.