If you slice it lengthwise, leave the core intact so the leaves hold together. This will make it easier to turn it.
Heat olive oil in heavy (preferably cast-iron) skillet over medium-high heat. Lay the radicchio quarters or slices in and sprinkle sea salt generously over it all. Leave it for 5-7 minutes. Maybe check it after four or five minutes to make sure it isn’t burning, but we want it to caramelize and brown, and get a little crispy even.
Turn it over when it gets to this point and add in the garlic in whatever form you have–you don’t want this to burn, it gets bitter. Try to stir the garlic during the remaining 5-7 minute cooking time so it browns lightly, but doesn’t burn. You may want to sprinkle a little more sea salt on this side, depending on how much you salted the other side.
Serve as is, or sprinkle a bit of cave-aged gouda or parmigiano over it. It’s great served with meat, if that’s your thing.