In a large bowl, whisk together the mayonnaise, relish, sugar, mustard, vinegar, salt, and pepper until smooth and well combined. Set the dressing aside. While the dressing rests, prepare all your vegetables and proteins: dice the ham into 1/2-inch pieces, cut the cheddar cheese into 1/2-inch cubes, finely chop the bell pepper into 1/4-inch pieces, mince the onion into small pieces, and chop the fresh parsley. Having everything prepped and ready will make the final assembly quick and efficient.
Bring a large pot of salted water to a rolling boil and add the bow tie pasta. Cook according to package directions (usually 9-11 minutes) until the pasta is al dente—tender but still with a slight firmness when you bite it. I find that Barilla holds its texture really well and doesn't turn mushy. Drain the pasta in a colander and rinse thoroughly with cold water to stop the cooking process and remove excess starch, which helps keep the salad from becoming too sticky.
In a large mixing bowl, combine the cooled pasta from Step 2 with the diced ham, cheddar cheese cubes, minced onion, peas, chopped bell pepper, and fresh parsley from Step 1. Pour the prepared dressing from Step 1 over the pasta mixture and toss gently but thoroughly until every piece of pasta and vegetable is evenly coated with the dressing. Use a large spoon or pasta fork to mix, being careful not to break the pasta.
Transfer the pasta salad to a serving bowl or storage container and refrigerate for at least 1 hour before serving. This chilling time allows the flavors to meld together and the salad to reach the perfect cold temperature. Give it a gentle stir before serving to redistribute the dressing, as some may settle at the bottom.