This is a delicious side dish that goes well with a wide variety of main courses. Use different cookie-cutter shapes for different occasions. Served with creamed spinach and Beef Tenderloin, it becomes a rare gourmet treat. To save yourself some time, the polenta can be prepared a day ahead and chilled overnight. Bake it when you're ready.
Bring the water to a boil and whisk in the polenta in a very thin stream. Stir constantly, allowing the mixture to return to a boil. Reduce the heat to low. Cover and continue to cook, stirring periodically. The polenta is done cooking when it forms a heavy mass. It should pull cleanly away from the sides of the pot when stirred.
Oil the bottom of a 9-inch pie pan and scoop the polenta into it, spreading in an even layer about 3/4 -inch thick. Cover with plastic wrap. Refrigerate for at least 30 minutes, or until firm.
Preheat the oven to 400 degrees F.
When the polenta is firmly set, cut it into shapes with a cookie cutter. For this dish, a heart-shaped cutter is perfect.
Press the oiled side of each shape into the grated cheese and transfer the shapes, cheese side down, to a lightly oiled nonstick skillet.
Bake in the oven for 15-20 minutes. When golden brown, turn the shapes out onto plates and serve browned side up.