Bring a large pot of generously salted water to a rolling boil. Add the tri-color rotini and stir once immediately. Cook according to package directions until al dente, about 9 to 11 minutes.
Drain the pasta in a colander and rinse thoroughly under cold running water until fully cool to the touch. Shake the colander well to remove excess water. Transfer the cooled pasta to your large mixing bowl.
In a separate bowl, combine the olive oil, red wine vinegar, pepperoncini brine, garlic, Italian seasoning, sugar, salt, black pepper, and red pepper flakes. Whisk vigorously until slightly thickened and emulsified.
Halve the cherry tomatoes and mozzarella pearls. Cut the salami into thin matchstick strips. Thinly slice the red onion and dice the red bell pepper into small pieces.
Add the tomatoes, mozzarella, salami, olives, pepperoncini, onion, and bell pepper to the bowl with the cooled pasta. Pour about three-quarters of the dressing over the top and toss gently until evenly coated. Hold back the remaining dressing for later.
Cover and refrigerate for at least 30 minutes. Just before serving, add the remaining dressing along with the parmesan and fresh basil. Toss once more, taste, and adjust seasoning. Add a splash of reserved pasta water if needed.