Grease a 9-inch tart or cake pan with a removable bottom with 1 teaspoon of the oil.
Heat 2 tablespoons of the oil in a large pot over high heat. When the oil is hot, add the onions, garlic, and basil and sauté for 30 seconds. Add the salt and pepper and sauté for another 30 seconds.
Stir in the milk and bring to a boil. Reduce the heat to medium and whisk in the Cheddar and Parmesan, just until the cheeses melt. Whisk in the cornmeal slowly, a little at a time, until the mixture has the consistency of a thick roux. Remove from the heat, and working quickly, spoon the mixture into the greased pan, spreading it and packing it down before it sets. Refrigerate for 1 hour.
Remove the polenta from the refrigerator, remove it from the pan, and cut it into 8 wedges. Heat the remaining 3 tablespoons oil in a large skillet over high heat. When the oil is hot, add the wedges of polenta and fry until golden brown, for about 1 minute on each side. Remove and drain on paper towels. Serve immediately.
Yield: 8 wedges