In a large skillet, heat 3 tablespoons of your chosen frying oil over medium heat. Add the chopped onions and cook, stirring occasionally, until they are soft and golden brown, about 10-12 minutes.
Once the onions are ready, add the sliced mushrooms to the skillet. Cook for another 8-10 minutes, stirring frequently, until the mushrooms release their moisture and become tender.
Transfer the sautéed onions and mushrooms into a food processor. Add the quartered hard-boiled eggs, shelled walnuts, salt, and black pepper. Pulse the mixture until it reaches your desired consistency.
Taste the mixture and adjust the seasoning if necessary. If you prefer a creamier texture, drizzle in the remaining 3 tablespoons of oil while the food processor is running until fully combined.
Transfer the Mock Chopped Liver to a serving bowl and refrigerate for at least an hour to allow the flavors to meld. Garnish with sliced scallions and/or butter lettuce if desired, and serve with matzo or your favorite crackers.