Soak liver: Rinse the liver and pat it dry. Cut it into strips, about 1.2 cm/ ½ inch. Place the pieces in a small bowl and cover with the cold milk. Soak for at least 30 minutes to one hour.
Potatoes (optional): While the strips are soaking, start making the mashed potatoes if you decide to serve the dish with potatoes. When the potatoes are done, make the mash while the other ingredients are still in the pan.
Onions: Slice the onions. Melt 1 tablespoon of the butter in a large skillet. Cook onions with a pinch of salt, frequently stirring, on medium heat during the last 10-15 minutes or so of the liver's soaking time. They should be golden brown and slightly caramelized, this will take 10 to 15 minutes. Adjust the taste with salt and pepper. Transfer them to a bowl and keep them warm while you cook the liver in the same skillet.
Prepare other ingredients: While the onions are cooking, peel, core (Note 5), and slice the apple into rings. Remove the liver from the milk and pat dry with kitchen paper. Place the flour on a large plate and turn the pieces into the flour. Pat gently to remove the excess flour. Set aside.
Cook apple rings: Melt another tablespoon of butter in a separate pan. Cook the apples for 3-4 minutes on each side until golden.
Fry liver: While the apples are cooking, melt the remaining butter in the pan you used for cooking the onions. Cook the liver on medium-high heat. It should be dark brown on the outside and with only a hint of pink on the inside. Check by cutting one piece in the middle. Don't overcook the liver, or it will be dry.
Finish dish: Return the onions to the pan, mix gently with the liver, and reheat shortly. Adjust the taste with salt and pepper. Sprinkle with fresh parsley or thyme if desired. (Note 6)