Preheat a broiler or fire up a grill. Cut the cooled polenta into 1 1/2" X 3" rectangles & brush lightly with olive oil. To grill, cook the polenta until it is lightly crispy & marked with the characteristic brown stripes on both sides.
To broil, set thepolenta on a broiler pan about 4" from the heat & broil, turning once, until the slices are golden & slightly crisp at the edges. Remove & set on a platter.
While the polenta is broiling, discard any bruised outside leaves of the radicchio, cut it in half lengthwise & then cut into quarters.
Wash & dry each piece carefully. Drizzle half the olive oil over the radicchio & season with salt & pepper. Set on an oiled broiler or on the barbecue. As the radicchio begins to soften & darken in colour, turn it to broil evenly.
Using your fingers or a knife, tear or cut the grilled radicchio into small pieces. Arrange over the polenta & drizzle with the rest of the olive oil & vinegar if you desire. Taste for salt. Add freshly ground pepper & serve hot or at rom temperature.