Preheat oven to 350 degrees F (175 degrees C). Butter a 9×13-inch baking dish.
Bring a large pot of lightly salted water to a boil. Cook cavatappi in boiling water, stirring occasionally, until cooked through but firm to the bite, about 8 minutes. Drain.
Melt butter in a large pot over medium-low heat. Whisk flour into butter until mixture has a thick, paste-like consistency, about 30 seconds. Slowly whisk 2 cups milk into butter-flour mixture until smooth. Stir in remaining milk, increase heat to medium high, and cook, whisking constantly, until mixture is thick and almost boiling, 5 to 10 minutes.
Stir Gouda cheese, Cheddar cheese, Swiss cheese, and 1 cup Parmesan cheese into milk mixture until cheese melts and cheese sauce is smooth. Fold cavatappi into cheese sauce; pour mixture into prepared baking dish.
Stir remaining Parmesan cheese and bread crumbs together in a small bowl. Sprinkle bread crumbs mixture over cavatappi mixture and drizzle truffle oil over the top.
Bake in the preheated oven until golden and bubbling, about 30 minutes. Cool for 10 minutes before serving.
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