Heat butter in a large skillet over medium heat. Add the sliced onions and cook for 5-8 minutes, stirring occasionally, until golden. Transfer to a plate.
In the same skillet, add the apple slices and cook for 3-4 minutes, stirring gently, until tender but not falling apart. Transfer to the plate with the onions.
Place flour in a shallow dish. Coat each veal liver slice in the flour and shake off the excess.
Add a bit more butter to the skillet if needed and increase heat to medium-high. Fry the coated liver slices for 2-3 minutes on each side, keeping the inside pink. Season with salt and pepper after cooking.
Arrange the liver slices on a serving plate. Garnish each slice with a spoonful of the cooked onions and three apple slices.
Pour the butter from the pan over the liver and sprinkle with chopped parsley.