Bring a large pot of salted water to a boil. Cook the cavatappi according to package instructions until al dente, then drain and let cool to room temperature.
While the pasta cools, prepare the dressing by whisking together the anchovies, garlic, balsamic-style vinegar, lemon juice, sea salt, and pepper in a mixing bowl.
Slowly drizzle in the olive oil while whisking to create a smooth, emulsified dressing.
In a large serving bowl, combine the cooled pasta with sun-dried tomatoes, capers, olives, salami, provolone, basil, and arugula.
Pour the dressing over the salad and toss everything thoroughly to coat.
For best results, cover and refrigerate the salad for at least 6 hours (or up to 24 hours) to let the flavors meld.
Before serving, give the salad a gentle toss and enjoy!