In 2-quart saucepan, place eggs in single layer. Add enough water to cover eggs by 1 inch. Heat to boiling. 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.
Meanwhile, in medium bowl, mix ham, bell pepper, onion, mayonnaise, ground red pepper, vinegar and mustard until well blended; set aside.
Drain water from eggs; peel eggs. Remove egg yolks from egg whites; place yolks in small bowl. Mash yolks; stir into ham mixture. Chop egg whites; stir into ham mixture.
Place lettuce on bottom halves of buns. Top each evenly with ham mixture and tomato slices. Cover with top halves of buns.