Cook tortellini according to package instructions until al dente. Drain, rinse under cold water, and toss with a teaspoon of olive oil. Transfer to a large bowl.
Whisk together olive oil, Dijon mustard, honey, minced garlic, oregano, salt, and pepper in a small bowl or jar.
Add salami, provolone, tomatoes, bell pepper, pepperoncini, olives, and red onion to the cooled tortellini. Pour two-thirds of the dressing over and gently toss to coat.
Cover and refrigerate for at least 30 minutes. Before serving, toss again, adjust seasoning, add remaining dressing if needed, and garnish with parsley/basil and Parmesan.
Notes
Make ahead up to 24 hours for best flavor melding.
Soak red onion slices in cold water for 10 minutes to remove bite if desired.
Substitute half the oil with Greek yogurt for a creamier dressing.