In a large pot, bring lightly salted water to a boil. Cook fusilli pasta until al dente, about 12 minutes. Drain in a colander, but do not rinse. Allow the pasta to cool for 5 to 10 minutes.

In a large bowl, mash the anchovy fillet and garlic into a paste. Whisk in red wine vinegar, mayonnaise, Dijon mustard, oregano, thyme, salt, and pepper. Slowly whisk in olive oil until the vinaigrette is smooth and coats the back of a spoon.

Toss the cooked pasta in the vinaigrette until well coated. Add in artichoke hearts, red peppers, olives, red onion, jalapeño, and pepperoncini. Mix in salami, pepperoni, provolone cheese, and ham until well combined. Cover and refrigerate for 3 to 12 hours.

Just before serving, stir in cherry tomatoes and parsley. Adjust seasoning if needed.