Place eggs in medium saucepan; cover with water. Bring to a boiling over high heat; cover and remove from heat. After 6 minutes, remove 2 eggs. Rinse with cold water; peel and set aside. Let remaining eggs stand in hot water 4 minutes more. Drain; rinse with cold water. Peel and coarsely chop the 10-minute eggs.
Meanwhile, in 12-inch skillet cook bacon until crisp; drain. Discard drippings and wipe pan with paper towel. Lightly toast both sides of bread slices in skillet. In small bowl combine mayonnaise and mustard.
Top 4 of the bread slices with basil leaves, chopped egg, and cucumber. Halve the remaining two eggs and place one half on each sandwich. Top with mayonnaise mixture, bacon and remaining bread slices. Serves 4.