How to Make It
Heat oil in a large, heavy, nonreactive skillet over medium. Add garlic; cook, stirring often, until fragrant and golden, about 2 minutes. Discard garlic. Add onion; cook, stirring often with a wooden spoon, until softened, about 4 minutes. Add wine and simmer until almost completely reduced, about 2 minutes. Add pancetta; cook, stirring often, until fat has rendered, about 4 minutes. Add radicchio, red pepper, and sugar; fold with tongs to combine and coat radicchio with the oil, about 2 minutes. Season to taste with salt and pepper.
Meanwhile, cook pasta according to package directions; drain pasta. Melt butter in pasta pot over medium. Return pasta to pot and add heavy cream, shaking pot and gently stirring to avoid tearing noodles, until pasta is coated, about 1 minute. Season with salt and pepper. Spoon pasta onto 4 plates and top with radicchio mixture. Top with shaved Parmigiano-Reggiano and serve immediately.