Cook cavatappi pasta in salted water until slightly undercooked. Drain and toss with olive oil to prevent sticking.
In a pot, combine heavy cream, whole milk, garlic, thyme, dry mustard, smoked paprika, and black pepper over low heat. Infuse flavors but do not boil.
Grate cheddar, gouda, mozzarella, and mix in a bowl. Crumble goat cheese separately.
Remove aromatics from the cream mixture. Add half of the cheese blend and goat cheese, stirring until melted.
Mix in cooked pasta until well coated with cheese sauce.
Layer half of the pasta in a baking dish, top with cheese blend, then add the remaining pasta.
Sprinkle grated parmesan cheese on top and broil until golden and bubbly.
Serve hot, enjoying the gooey cheese pull and crispy top. Be cautious of hot cheese.
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