Bring a large pot of salted water to a boil and cook the pasta according to package directions. Reserve 1 cup of pasta water before draining.
While the pasta cooks, simmer the apple cider in a small saucepan until reduced by about half, 10 to 12 minutes.
In a large skillet, melt the butter over low heat. Add the anchovies and mash with a spoon until fully dissolved, about 2 minutes.
Add the garlic and cook 30 seconds until fragrant.
Pour in the reduced apple cider and let it bubble for 1 minute.
Lower the heat and stir in the heavy cream. Simmer 2 to 3 minutes until slightly thickened.
Add the drained pasta and Parmesan, tossing to coat. Add reserved pasta water a splash at a time until the sauce clings smoothly.
Season with black pepper, scatter parsley on top, and serve immediately with extra Parmesan.