Whisk together all the dressing ingredients and set aside.
Put the dressing together first so it's good to go when the radicchio is ready!
Leaving the core intact, cut each radicchio in halves or quarters if large heads.
Brush with half of the oil.
Sprinkle with half of the sea salt and half of the freshly ground pepper.
Grill on high heat, uncovered.
Turn often but allow edges to crisp up (slightly charred not black!)
Remove from the grill to a cutting board.
Chop the radicchio into bite sized chunks.
Toss with the basil and parsley (or other greens ~ wild if possible)
Add the dressing and combine lightly.