Boil the water. Bring a large pot of water to a rolling boil and stir in the 1 tablespoon of salt.
Cook the pasta. Boil the pasta for 1 to 2 minutes less than the package directs, until just al dente with a firm center. Scoop out 1/2 cup (120 ml) of the cooking water, then drain.
Soften the onion. While the pasta cooks, melt the butter in a deep 12-inch skillet over medium heat. Add the onion and cook for 5 minutes, until soft and translucent, then add the garlic and cook for 30 seconds.
Bloom the paprika. Stir in the smoked paprika and cook for 30 seconds, until the butter turns deep red and smells smoky. Do not let it darken or smell sharp.
Add the broth. Pour in the broth, scrape up anything stuck to the bottom, and simmer for 3 minutes, until slightly reduced.
Add the cream. Stir in the cream and simmer gently for 4 to 5 minutes, until the sauce coats the back of a spoon and a line drawn with a finger holds its shape.
Warm the pork. Lower the heat, add the pork and stir for 2 to 3 minutes, until the meat is steaming hot all the way through.
Melt in the cheese. Take the pan off the heat and stir in the Parmesan a handful at a time, until the sauce looks smooth and glossy.
Toss with the pasta. Add the pasta and 1/4 cup (60 ml) of the reserved pasta water, then toss for 1 minute over low heat. Add more pasta water, a splash at a time, until the sauce clings to the pasta without pooling.
Finish. Stir in the vinegar, then taste and add salt and pepper as needed. Top with parsley and extra Parmesan and serve right away.