Place the potato halves in a large pot and fill with cold water enough to just cover the potatoes.
Cook over medium heat until fork-tender, about 20 to 25 minutes.
Drain well, spread onto a rimmed baking sheet and refrigerate until cold.
Cut the bottom fibrous portion of asparagus off and discard, about an inch.
In a large pot of salted, boiling water, blanch the asparagus by lowering it into the boiling water and cooking for 2 minutes.
Remove from boiling water and immediately plunge the asparagus into ice water to stop the cooking process and chill; set aside.
Cook the penne pasta according to package directions.
When al dente, drain and run under cold water until thoroughly cooled. Place pasta into a large mixing bowl.
In a medium jar with a tight fitting lid, combine all dressing ingredients and shake well to combine.
Add cooked potatoes, asparagus and green onion to the pasta and toss lightly to combine.
Dress with desired amount of dressing and toss to coat.
Stir in shaved parmesan.
Adjust seasoning with salt and pepper to taste.
Serve at room temperature or cold.