Preheat the oven to broil, and place a rack four inches below the heating element.
Bring a large pot of water to a boil, and season generously with salt. Add the cavatappi, and cook according to the package instructions, stopping two minutes before al dente. Drain the pasta, and drizzle a bit of olive oil over the top. Toss to combine and coat the pasta with the oil, and set aside.
kosher salt, 1 pound cavatappi noodles
In the same pot over medium heat, add the heavy cream, milk, black pepper, mustard, thyme, paprika, and garlic cloves. Stir to combine and bring to a very gentle simmer. Simmer for 20-25 minutes, or until the flavors have married and the dairy is slightly reduced. Set a fine mesh strainer over a large mixing bowl. Pour the infused cream through the strainer and discard any solids. Bring the cream back up to a simmer.
3 cup cream, 2 cup milk, ½ teaspoon black pepper, 1 teaspoon dry mustard, 1 large bunch thyme, ¼ teaspoon smoked paprika, 5 garlic clove
While the cream is coming to a simmer, add the cheddar, mozzarella, and gouda to a medium mixing bowl. Toss well to combine.
½ pound sharp white cheddar, ½ pound whole milk mozzarella, 1 pound gouda
Add half of the cheese mixture, as well as the goat cheese, to the cream mixture on the stove. Stir gently to melt the cheese. Once the cheese is melted, add the macaroni and stir to incorporate. Bring the mixture back to a simmer, then remove from the heat.
1 log goat cheese
Add half of the mac and cheese mixture to a lightly greased 9x13 pan. Then, sprinkle the remaining half of the cheese over the top of the macaroni. Spread the final portion of macaroni over the top, and sprinkle the grated Parmesan cheese evenly over the macaroni.
½ cup grated Parmesan
Place the pan on a sheet tray. Transfer it to the oven, and broil for five to ten minutes, rotating it frequently to allow for even browning over the top. Once the top is deeply golden brown and bubbling, remove it from the oven, and allow it to cool for at least 15 minutes.
Serve immediately while warm.