Bring a pot of water to a boil, then add cubed red potatoes and cook until tender, about 10–12 minutes, with the water at a steady boil and potatoes easily pierced. Drain the potatoes and spread them on a sheet pan to cool, using a cool, even layer so they don’t steam.

In a serving bowl, combine cooled potatoes, diced salami, cubed mozzarella cheese, halved cherry tomatoes, sliced pepperoncini, and finely diced red onion, tossing until the mix looks evenly distributed. Add Italian dressing and toss again so the potatoes look glossy and coated.

Sprinkle chopped fresh basil and grated Parmesan cheese over the top, then toss gently until basil is speckled throughout and Parmesan clings lightly to the dressing.

Season with salt and black pepper to taste, then toss one more time, looking for a balanced seasoning throughout the bowl.

Cover and refrigerate for 2 hours before serving, until chilled throughout and the flavors look settled and cohesive.