Bring a large pot of generously salted water to a boil, add the pasta and cook until al dente. Scoop up 1/2 cup cooking water and drain the pasta.

While the pasta is boiling, prepare the sauce. Heat oil in a large pan over low heat. Add the garlic and tomato paste and cook for 30 seconds. Then add the butter and allow to melt before adding the nduja paste and whisking well.

Add vodka, stir and simmer for 2 minutes over low. Pour in cream and cook for 30 seconds, Bring to a simmer. Stir in Parmesan, add the pasta and ¼ cup cooking water, toss to combine. Stir until the sauce thickens slightly, and the pasta is coated with a silky saucy layer. If the sauce is too thick, add some of the remaining pasta water, if needed. Finish off with black pepper. Serve immediately!