Turn on the broiler to high.
Wash and drain radicchio heads and cut in fourths, lengthwise, leaving them attached at the root.
Coat the bottom of a 9" x 11" baking dish with 1 tbsp. olive oil and place the radicchio pieces in the dish, side by side.
Drizzle the radicchio pieces with olive oil, and season with salt and pepper.
Place under the broiler for 5 minutes, and then turn each radicchio wedge over and broil for 5 more minutes. Keep an eye that they don't burn. The outer leaves will brown a bit and the head will soften.
To serve: Cut a wedge of hot polenta and place on a plate. Place a wedge of radicchio on top. Garnish with a drizzle lemon juice, finishing salt or sea salt, and a few sprigs of mint. Finally, douse generously with olive oil.