To a saucepan, add broth, oil, and salt. Bring to a roiling boil.
Begin to whisk in the cornmeal slowly. Once all the cornmeal has been added, turn the heat down to medium-high and continue to stir the mixture until it resembles mashed potatoes. This can take approximately 15-20 minutes.
Remove the saucepan from the heat and spread the polenta into a greased 9" x 9" baking dish. Transfer the dish to the refrigerator to chill for 1 hour.
After 1 hour, remove the polenta from the fridge and slice into 12 rectangles.
Transfer each rectangle to a well-greased, hot grill pan. Grill each side for a minute or two and then transfer to a serving plate. Top with fresh tomatoes and basil or tomato sauce.
Alternatively, if you are not using a grill pan, add a tablespoon of butter or olive oil to a frying pan and sauté each rectangle until golden on each side. Top with fresh tomatoes and basil or tomato sauce.