Trim any membrane or skin from the calf liver. Slice it into thin strips for quick cooking and tender results.

Thinly slice the onions into half-moon shapes. Heat butter and olive oil in a wide skillet over medium-low heat. Add the onions and cook gently for 15 minutes, stirring occasionally until they are soft and translucent. Add a splash of water or wine to help them soften without browning.

Once the onions are caramelized, push them to the sides of the skillet. Increase the heat to medium-high and add more olive oil. Quickly add the liver strips and sear them for about 1-2 minutes, just until they lose their raw red color and stay pink inside.

Mix the liver with the onions. Add chopped parsley, salt, and pepper to taste. Let it cook for another minute.

Pour a splash of white wine into the hot skillet to deglaze. Scrape up any browned bits from the bottom of the pan. Let the wine reduce until it becomes a syrupy sauce.

Plate the liver and onions, pouring the pan sauce over the top. Serve with soft polenta, grilled polenta, crusty bread, or steamed potatoes. Garnish with lemon wedges and fresh parsley if desired.