Rinse your fresh beef liver under cold kitchen water. Pat the pieces dry with clean paper towels very carefully. Remove any tough outer membrane using your sharp chef knife.

Slice the meat into even half-inch thick strips now. This size ensures the meat cooks quickly and stays tender. Place the strips onto your clean dry cutting board.

Mix the all-purpose flour with salt and black pepper. Dredge each meat piece in the seasoned flour mix gently. Shake off any extra flour before moving to the pan.

Heat your olive oil in the large frying pan. Add the sliced white onions to the hot oil carefully. Cook them for five minutes until they look soft brown.

Push the sweet onions to the side of the pan. Place the floured meat strips into the center space. Sear them for two minutes without moving the pieces around.

Flip the meat pieces over using your cooking tongs. Cook the other side for two more minutes only. Add the unsalted butter to the hot pan now.

Pour the balsamic vinegar over the meat and onions quickly. Stir everything together to create a rich glossy pan sauce. Sprinkle fresh parsley on top and serve it hot.