Bring a large pot of salted water to a boil. Add the 16 oz of Farfalle pasta and cook according to package instructions until al dente (usually about 10 minutes). Drain and rinse under cold water to cool.
While the pasta boils, halve the 2 cups of cherry tomatoes, quarter the 8 oz of sliced beef salami, slice the 1 cup of black olives, finely dice the 1/2 cup of red onion, and chop the 1/4 cup of fresh parsley.
In a small bowl, whisk together 1/4 cup olive oil, 2 tbsp red wine vinegar, and 1 tbsp Italian seasoning until emulsified.
In an extra-large serving bowl, combine the cooled pasta, tomatoes, beef salami, olives, red onion, parsley, and 8 oz of mozzarella balls.
Pour the dressing over the pasta mixture. Toss gently until all ingredients are evenly coated. Cover and refrigerate for at least 1 hour before serving.