Grease a 9-inch square baking pan 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 saute for 30 seconds. Add the salt and pepper and saute for another 30 seconds. Stir in the milk and bring to a boil. Whisk in the polenta slowly, a little at a time, until the mixture has the consistency of a thick roux. When the mixture is thick, add the blue cheese and stir until it is melted and incorporated. 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 pan and cut evenly into1 1/2-inch squares. Dredge the polenta squares in the flour. Heat the remaining 3 tablespoons oil in a large skillet over high heat. When the oil is hot, add the polenta squares and fry until golden brown, about 45 seconds to 1 minute on each side. Remove and drain on paper towels. Arrange arugula leaves on each square and top with the caramelized onions and nuts.
Yield: 36 small squares (Note: If preferred, instead cut the polenta into larger squares for appetizer portions or as a main course accompaniment.)