Skin the sunchokes using a small paring knife or a swiveling-blade peeler, wash them in cold water, then slice them into disks about ¼inch thick.
If you are using the long Treviso radicchio with an extended root, pare it down to a short nub. If the root has been cut off, as it is in the endive, trim away a thin slice from the butt end. Detach the leaves from the radicchio or endive, discarding any blemished ones, shred them lengthwise into narrow strips about ¼inch wide, soak briefly in cold water, and drain. If you are using a round, cabbage-like head of radicchio, shred it very fine, soak briefly in cold water, and drain.
Put the olive oil and garlic in a medium sauté pan, turn on the heat to medium strength, and cook, stirring frequently, until the garlic begins to sizzle. Quickly put in the sliced sunchokes and shredded radicchio or endive, adding salt and liberal grindings of pepper. Cover the pan; turn the heat down to low; and cook, turning over the vegetables from time to time, until the sunchoke feels tender when prodded with a fork, about 40 minutes.