MAKE THE SALAD: In a large serving bowl, combine the cucumber, tomatoes, olives, red onion, pepperoni, mortadella, salami, mozzarella and basil and gently toss to combine.
Bring a large pot of salted water to a boil; cook the cavatelli in the boiling water according to the package directions, until al dente.
Drain the pasta and run cold water over it until completely cooled.
Add the pasta to the serving bowl and gently toss to combine.
MAKE THE DRESSING: In a medium bowl, whisk the pepperoncini and brine, honey, mustard, pecorino, oregano and pepper to combine.
Add the vinegar and whisk to combine.
Slowly drizzle in the oil, whisking constantly, to emulsify.
Pour the dressing over the pasta salad and gently toss to combine.
Let sit for 30 minutes, then gently toss again and serve.