Soak 4 wooden skewers in water 15 to 20 minutes to prevent scorching. Preheat a grill to medium high. Combine the pork, bell peppers, red onion, 3 tablespoons olive oil, 2 tablespoons cherry pepper brine, the oregano and 1/2 teaspoon salt in a large bowl; toss.
Meanwhile, bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Drain and rinse under cold water; transfer the pasta to a large bowl and add the cherry peppers, the remaining 3 tablespoons olive oil and 2 tablespoons brine, and 1/4 teaspoon salt; toss.
Thread the bell peppers, pork and red onion, alternating, onto the skewers. Drizzle any remaining marinade over the kebabs. Brush the grill grates with olive oil. Grill the kebabs, turning occasionally, until the pork is cooked through and the vegetables are well marked, 10 to 12 minutes.
Add the basil, parsley and bocconcini to the bowl with the pasta; season with pepper and toss. Serve the kebabs with the pasta salad.