Trim the liver of its outer covering, blood vessels, and any blemishes. Pat dry, cut in julienne strips (2” x ½” x ½”), and set aside.
Slice the onions thin, working with the grain. In a nonreactive skillet, melt the sugar until it caramelizes, add the onions and bay leaves, and mix well. Add 3 tablespoons of olive oil, the salt and pepper, and sauté over moderately high heat until the onions are golden brown but not limp. Stir in the flour, blending well, add the vinegar and wine, and simmer about 2 minutes, until the sauce thickens.
Meanwhile, in a skillet large enough to hold the strips of liver in a single layer (use two pans if necessary), heat the vegetable oil, add the liver, and sauté, stirring occasionally, about 2 minutes.
With a slotted spoon, drain the liver and transfer it to the sauce, tossing gently until well coated, about 1 minute. The sauce should be quite adhesive, not runny.
Serve immediately with boiled or fried polenta.