Bring a large pot of lightly salted water to a boil. Cook fusilli in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain thoroughly in a colander, but do not rinse; stir to release heat. Cool in the colander for 5 to 10 minutes.

Meanwhile, mash anchovy fillet and garlic into a paste in a large bowl with a whisk or fork. Whisk in vinegar, mayonnaise, Dijon mustard, oregano, thyme, salt, and black pepper to combine. Slowly drizzle in olive oil, whisking constantly, until smooth, thick, and vinaigrette coats the back of a spoon.

Toss pasta into bowl with vinaigrette until well coated.

Toss in artichoke hearts, red peppers, black olives, green olives, red onion, jalapeño, and pepperoncini. Stir in salami, pepperoni, provolone cheese, and ham; mix thoroughly to combine. Cover bowl with plastic wrap; refrigerate until well chilled, 3 to 12 hours.

Stir in tomatoes and parsley; mix thoroughly. Taste; adjust seasoning if needed.