Place eggs in a medium saucepan in a single layer. Add enough water to cover eggs by 1 inch. Bring to a boil over high heat. Reduce heat to medium and simmer for 10 minutes. Remove eggs with a slotted spoon and plunge them into an ice-water bath (to prevent further cooking). Shell the eggs and chop them into 1/2-inch pieces. Set aside.
Meanwhile, in a large bowl, combine next 7 ingredients. Make sure to dice the red peppers and parsley. You also want to drain the capers.
Mix well. Add eggs and mix gently to combine. Spoon egg salad onto 4 bread slices. Top with lettuce leaves and second slice of bread.