Pour water in a big pasta pot, add a pinch of salt and bring to a boil. When boiling, add pasta, reduce heat and cook per package instruction (this type of pasta usually between 8-10 minutes).
Peel onion and slice. Wash radicchio and dry, then cut into strips. There should be a rather generous amount of it (the more the better), as the radicchio will shrink when cooking. Cut prosciutto slices into large strips or cuts.
While the pasta is cooking, heat olive oil in a pan, then add sliced red onions and stir-fry for a couple of minutes, until the onions tenderize. Don't worry if they get slightly burnt. Even better if you have the time to caramelize them. When the onions soften, add in prosciutto and fry it on either side until crips. Remove onions and prosciutto from the pan to stop burning it, then pour in white wine and let it cook out to reduce the alcohol amount.
As the wine cooks, scrape the bottom of the pan with a spatula, to release the proteins and bind the sauce. Add the onions and prosciutto back in and add also radicchio strips, stirring while it cooks and shrinks.
When the pasta is done, save a small glass of pasta water, then drain the pasta. Add cooked pasta to the prosciutto and radicchio pan, mix well and add a splash of pasta water. The pasta water will help bind the sauce, make it creamer and stick to the pasta. Top with grated aged cheese, parmesan and salt & pepper to taste. Serve hot.