Peel and mince 3 shallots and saute in 1 tablespoon butter until soft and fragrant. Add 2 tablespoons minced fresh sage, stir, and remove from the heat. Add to the polenta with the pepper, butter, and cheese.
Prepare the sage-shallot polenta several hours in advance. When it is done, pour it onto a baking sheet rinsed in cold water and use a rubber spatula to spread it 3/4-inch thick. Let it cool slightly and then place it in the refrigerator, covered, until it is very firm. Remove it from the refrigerator, cut it into small cubes, and place the cubes in a medium mixing bowl. Add the minced sage and the pancetta, toss lightly, and set aside.
Preheat the oven to 350 degrees. Rinse the game hens inside and out, dry them thoroughly with a clean tea towel, and set them on end, central cavity down, on absorbent paper or toweling so that excess moisture can drain out. Let them sit for 5 minutes. Stuff the hens one by one. Turn the hen on end, with the cavity facing you. Season the inside with salt and one or two turns of black pepper, and then fill the cavity with about 1 cup polenta mixture. When all the hens have been stuffed, loosen the breast skin by extending your finger under the skin to loosen the membrane. Insert 2 sage leaves under each side of the breast skin of each hen and then truss or tie the hens tightly with string to close the cavities. Pour a little olive oil in the palm of one hand and rub the olive oil over the surface of the hen's skin. Season each with several turns of black pepper and a little salt. Set the hens on a roasting rack, place in a baking pan, and roast for approximately 1 hour. Remove from the oven, remove the string, and serve immediately.
Recipe courtesy of Gourmet Magazine