Boil milk, oil, and salt in a large pot. Add the cornmeal and stir until thick. This should take about ten minutes. Stir in the cheese. Pour the mixture into a greased cookie sheet, in a layer no more than half an inch thick. You might fill one and a half cookie sheets. Let the polenta cool.

Preheat oven to 425°F.

While the polenta is cooling, make the sauce: in a food processor, coarsely grind the garlic, basil and onion. Transfer to a bowl and stir in the remaining sauce ingredients.

Grease an 11-by-14-inch lasagna pan. Make one layer polenta, making sure you leave no blank spaces. Add half the sauce. Repeat: one layer polenta, one layer sauce. Bake the casserole for about 45 minutes, or until the dish looks bubbly and hot. Mix the bread crumbs with the butter, and sprinkle over the dish. Bake another 10 minutes. Let cool slightly before cutting into squares.