Cook the tortellini according to package instructions. While the pasta is cooking, make an ice water bath: Dissolve the 1 tablespoon kosher salt in 1/2 cup warm water in a large bowl. Add 4 cups each ice and water and reserve. Drain the pasta, cool in the ice water bath for 2 minutes, then drain again.
In a large bowl whisk the oil, vinegar, and mustard. Add the pasta, olives, peppers, salami, cheese, pepperoncini, and parsley and toss to combine. Season with salt and pepper to taste.