Heat oil in large ovenproof nonstick skillet on medium heat. Add onion and asparagus; cook and stir 2 minutes. Reduce heat to medium-low.
Beat eggs, milk, dill, salt and pepper in medium bowl. Stir in smoked salmon. Pour into skillet. Cook without stirring 5 minutes or until eggs are set on bottom. Sprinkle with cheese.
Broil 4 to 5 minutes until eggs are set and cheese is lightly browned. Sprinkle with additional dill, if desired.
Wrap the skillet handle in foil if your skillet is not ovenproof.