Step 1Rinse liver and gently dry. Cut each slice in half and season with salt and pepper. Set aside.
Step 2Heat oil and butter over medium heat and add onion. Cook, stirring frequently, until golden brown, about 10 to 12 minutes.
Step 3While onion cooks, dredge liver in flour and gently shake off any excess. When onion slices have browned, push them to side of pan and add liver. Cook liver 1 to 2 minutes per side for medium rare.
Step 4Pour balsamic vinegar over liver and onions about 30 seconds before liver is done. Serve at once.