Bring a large pot of well-salted water to a boil and cook the farfalle until just tender (al dente). Drain, rinse under cold water to cool quickly, and shake well to remove excess water.
In a bowl, whisk together the mayonnaise, Greek yogurt, Dijon, vinegar, honey, garlic powder, smoked paprika, salt, pepper, and chopped pickles until the dressing is smooth and cohesive.
Add the cooled pasta to a large mixing bowl, then scatter in the ham, cheddar, corn, cucumber, red bell pepper, celery, and green onions (and parsley, if using). Toss gently to distribute the mix-ins evenly.
Pour the dressing over the pasta mixture and fold until every bow tie is coated. Cover and refrigerate for at least 1 hour so the flavors meld.
Before serving, stir once more and taste for seasoning, adding a pinch more salt or a small splash of vinegar if you want extra tang.