Place eggs in small saucepan; add enough cold water to cover eggs by 1 inch. Bring to a boil. Immediately remove from heat; cover and let stand 15 minutes. Drain; rinse with cold water. Place eggs in bowl of ice water; let stand 10 minutes. Peel eggs; slice. Set aside.
Meanwhile, wash asparagus; snap off tough stem ends. In large skillet, bring 1 inch lightly salted water to a boil. Arrange asparagus spears evenly in skillet. Cover; cook 4 to 5 minutes or until asparagus is crisp-tender. Drain; rinse with cold water to cool.
In small bowl, combine mayonnaise, mustard and dill; blend well. Spread mixture on 1 side of each bread slice. On 2 bread slices, spread side up, layer egg slices and asparagus; top each with second bread slice. Layer tomato slices, cheese and lettuce on each sandwich; top with remaining bread slices, spread side down. If desired, place 2 decorative toothpicks in each sandwich.