Fill a large pot with about 4 quarts (3.8 liters) of water and bring to a vigorous boil over high heat. Add 1 tablespoon of salt to season the pasta water.
Add the rotini to the boiling salted water, stir immediately, and cook according to package directions until just al dente. Taste 1-2 minutes before the timer goes off to check for doneness.
Drain the pasta through a colander and rinse under cold running water for at least 60 seconds, tossing to ensure even chilling. Shake well to remove excess water and spread out to air dry for 5-10 minutes.
In a medium bowl, whisk together mayonnaise, apple cider vinegar, Dijon mustard, sugar, garlic powder, onion powder, salt, and pepper until completely smooth. Taste and adjust seasoning as needed.
Dice the ham into ½-inch cubes, thinly slice the celery on a slight diagonal, finely dice the red onion, and ensure peas are fully thawed and drained. Cube or shred the cheddar cheese.
Transfer cooled pasta to a large mixing bowl and add the ham, celery, red onion, peas, and cheddar. Pour the dressing over everything and gently fold until every piece is well coated.
Cover tightly and refrigerate for at least 1 hour, preferably 2 hours or overnight. Before serving, stir well and add extra mayonnaise if the salad looks dry. Garnish with parsley if desired.