Place the liver in a mixing bowl. Cover with water and let it soak for 15 to 20 minutes.
In a large cast-iron skillet, melt the butter over medium-low heat. Add the onions and cook, while stirring occasionally, until tender and lightly browned. Remove from the skillet and season to taste with salt.
In a shallow bowl, whisk together the milk and eggs until well blended. Place the bread crumbs on a plate.
Rinse the liver under cool running water and then pat dry with paper towels. Lightly season each side with salt and pepper. Dip into the milk mixture, then into the bread crumbs, coating evenly.
Pour the oil into the skillet that you used for the onions, and turn the heat to medium heat.
After the oil has heated, add the liver and cook 2 to 3 minutes on each side or until cooked through. Top with the onions.