Cut the Parmesan cheese into large pieces. Peel and chop the garlic. Chop walnuts coarsely, except for 8 halves. Wash parsley, dab dry and, except for something to garnish, pluck leaves from the stalks.
Do not puree parmesan, walnuts, parsley and 1 pinch of salt too finely in the universal chopper, adding the oil little by little. Cook the tagliatelle in plenty of boiling salted water for 8-10 minutes. In the meantime clean, wash and drain the radicchio.
Put 4 beautiful leaves aside. Cut the rest of the radicchio into fine strips. Drain tagliatelle, quench and mix with pesto and radicchio strips. Arrange tagliatelle in radicchio leaves in portions and decorate with parsley and walnuts.