Toss the kale and radicchio with about half of the oil, lemon juice and zest in a large glass mixing bowl. Let stand about 2 minutes. Add the Pecorino, currants, basil and the remaining oil, lemon juice and zest. Thoroughly mix. Season with salt and pepper. Set aside.
Fold in the walnuts just before serving and top the salad with a pile of Pecorino.