1. Heat oil in a heavy skillet; add chopped onion. Cook over medium high heat until translucent and golden brown. Remove and set aside.
2. Melt butter in the skillet; add sliced beef liver. Over medium heat, fry the liver about 3 minutes on each side. To test for doneness, cut the liver. If pink, continue cooking for 30 to 60 seconds.
3. Place the cooked liver and the cooked onions in a blender or food processor. Grind coarsely. In a medium bowl, combine the liver/onion mixture with mashed hard-boiled egg, salt, and pepper.
4. Refrigerate overnight then serve with sliced tomato, sliced cucumber, and rye bread.