Here is a recipe I learned long ago when I was living in the Veneto, where radicchio is used more in cooking than in salads. It is basically a paste or pate' made from radicchio and walnuts, except that I find that our native pecans work better because they are slightly sweeter. Of course, if you insist on walnuts, go right ahead.
Now. Take an average head of radicchio as can be commonly found in American markets (see photo). Wash and shred. Place about three tablespoons of olive oil in pan, saute' clove of garlic until it colors (never brown). Remove garlic and saute' the radicchio in oil. The veggie will change color and lose volume. When the color has in fact changed, add salt and pepper. Place radicchio in blender with two handfuls of pecans. If you find that the final paste is a bit too bitter, add a little sugar. A little.
This will work on crusty bread or crackers or as a sauce for short pasta (in which case you might add a smidgen of white wine to the blender, or other embellishments of your choice).
If you are a radicchio lover (and you should be), find more info and recipes at this authentic site dedicated to the veggie.