Combine all of the dressing ingredients in a small mixing bowl and whisk to combine. Set aside (or refrigerate if making ahead).

Cook the tortellini according to package directions. Rinse well with lots of cold water in a strainer, and drain.

Add half of the tortellini to a large mixing or salad bowl and drizzle a little of the dressing over it. Add the remaining pasta and drizzle a little more.

Add the salami, pepperoni, ham, red peppers, peperoncini, another drizzle of dressing, and, using tongs, fold into the tortellini, taking care not to rip or squoosh the pasta too much.

Add the mozzarella and about half of the parmesan cheese to the bowl and carefully fold in with the tongs. Taste a forkful of the salad to determine whether there's enough dressing at this point. If it's a little dry, add another drizzle (but not too much).

Cover the salad bowl and refrigerate for at least two hours (refrigerate the dressing, too).

Before serving, drizzle more dressing over the entire tortellini salad and fold in. The pasta should be glossy, but not drowning in dressing. Serve any leftover dressing with the meal so that your guests can add more if they want.

Sprinkle the black pepper and Italian herbs over the salad, followed by the remaining parmesan cheese.