Bring a large pot of lightly salted water to a boil. Cook the rotini in boiling water until tender yet firm to the bite, about 8 minutes; drain. Rinse pasta with cold water until chilled; drain.
Mix carrots, pepperoncini, Genoa salami, Cheddar cheese, provolone cheese, sweet onion, green olives, Kalamata olives, pepperoni, celery, green bell pepper, red bell pepper, and artichoke hearts together in a large mixing bowl. Pour Italian-style salad dressing over the salad and toss to coat; add pasta and stir.
Cover bowl with plastic wrap and refrigerate for at least 1 hour before serving. Stir salad and add more Italian-style dressing as needed if you find the salad too dry.
