Slice onion into 1/16-inch slices. Melt half of the butter in a pan over medium heat. Add the onion and lightly brown. Add the broth and simmer over low heat.
Remove the skin and veins from the liver. Thinly slice the liver. Dredge slices in flour. Sauté the liver slices briefly in a pan with the remaining butter. Add a small amount of white wine. Add the onions, salt and pepper.
Garnish with chopped parsley before serving. For the polenta, slowly sprinkle yellow cornmeal into 1 quart of salted boiling water, whisking continuously. Cook over low heat for at least 30 minutes, stirring with a wooden spoon.