Cut tips off asparagus, about 1-inch long (you should have 1/2 cup). Save remaining stalks for another recipe. Bring small pot of salted water to a boil. Cook asparagus tips until just tender, 2 to 3 minutes. Drain, refresh under cold water, drain well and pat dry. Reserve.
Combine chopped eggs in bowl with dill, salt and pepper. Stir in mayonnaise and mustard. Gently fold in asparagus tips. Cover and refrigerate up to 4 hours. Serve with toasted bread, if desired.