1 Slice The Head Of Radicchio In Half, Then In Quarters. Take Each Quarter And Cut Slices Of About 1/2 Inch Thick Crosswise On The Radicchio From The End Toward The Core. Discard The Cores. Cut The Belgian Endives Into 1/2-Inch Thick Slices, Also Discarding The Hard Inner Cores. Cut The Stems And Fronds Off The Fennel And Set Aside. Slice The Fennel Bulb In Half And Then In Quarters. Cut Thin Slices From Each Quarter Toward The Core. Cut Out And Discard The Core. Toss All The Cut Vegetables In A Large Bowl With The Grated Parmesan. 2 To Make The Vinaigrette, Chop The Fennel Fronds You Cut Off The Bulb And Put 3 Tablespoons Worth Into The Bowl Of A Blender. Add The Mustard, Shallot Or Onion, Lemon Juice, Salt And Sugar. Pulse To Combine. Scrape Down The Sides Of The Blender Bowl And Put The Lid Back On Without The Center Stopper. Cover The Stopper With Your Hand As You Start The Blender Again. Drizzle In The Olive Oil And Puree The Dressing For 30-45 Seconds. Pour Over The Vegetables And Toss To Combine.