Slice your radicchios in two, then in two again. In a pan, heat some oil (olive or neutral). You want to use enough to coat the bottom of the pan. Let it get comfortably hot, it has to sizzle !
In the meantime, season the radicchio by sprinkling some salt on the sides and between the leaves. Once the oil is hot place the wedges in getting a nice char on both sides (about 1 minute on each side but it will depend on your pan, the size of your wedges etc..). Once all the wedges are grilled and off the pan, place them on absorbent kitchen paper (or, like me, toilet paper if you have none..) while you make the dressing.
Simply blend or mix all the ingredients in a mixer, blender, or by hand if electricity fails you (smash the cheese with a fork first, then whisk in the vinegar first, the oil after).
To serve, either place three to four slices with a generous drizzle of sauce on each plate or family style on a big serving dish. I like to grind some fresh pepper on top right before serving and garnish with some cress, ruccola or other green leaf for a little pop of color and bitterness.