Rinse the chicken livers under cold water and gently pat dry with paper towels. Trim away any visible fat, veins, or greenish spots, which can taste bitter. If desired, soak the livers in milk or water for 20–30 minutes to mellow the flavor, then drain and pat dry thoroughly.

In a large skillet, heat 2 tablespoons of schmaltz over medium-low heat. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, for 20–30 minutes until the onions are very soft and deeply golden. If they begin to brown too quickly, reduce the heat and add a tablespoon of water to prevent burning.

When the onions are richly caramelized, scoop out about 1/4 cup and set aside for garnishing the finished chopped liver. Leave the remaining onions in the pan.

Increase the heat under the pan with the remaining onions to medium. Add the chicken livers and, if using, the brandy or dry sherry. Cook for 5–7 minutes, turning the livers occasionally, until they are browned on the outside but still just slightly pink inside. They should be cooked through but not dry; when cut open, the center should be barely pink, not red.

While the liver and onion mixture is still hot, season with kosher salt, black pepper, and garlic powder. Toss gently to distribute the seasonings evenly so they absorb into the mixture.

Transfer the cooked liver and onion mixture to a large bowl or food processor. Let it cool for about 10 minutes so the residual heat does not overcook the eggs when they are added.

Roughly chop the hard-boiled eggs and add them to the cooled liver and onion mixture.

For a smooth liver pâté–style spread, pulse the mixture in a food processor until mostly smooth, scraping down the sides as needed. For a rustic, deli-style chopped liver, transfer everything to a wooden board and chop by hand with a large knife or mezzaluna until finely mixed but still slightly chunky.

Stir in the remaining 1 tablespoon of schmaltz (and an additional tablespoon if you prefer richer liver). If the mixture seems too thick or dry, add 1–2 tablespoons of cold water or chicken broth, a little at a time, until you reach your desired spreadable consistency.

Taste the chopped liver and adjust the seasoning with more salt, pepper, garlic powder, or a pinch of paprika as desired. Remember that the flavors will mellow slightly after chilling. If using fresh parsley, stir it in now.

Transfer the chopped liver to a serving dish or an airtight container. Smooth the top, cover, and refrigerate for at least 2 hours, or ideally 4–8 hours or overnight, to allow the flavors to meld and the texture to set.

Before serving, let the chopped liver sit at cool room temperature for 20–30 minutes so it is not ice cold. Top with the reserved caramelized onions, a sprinkle of fresh parsley, and flaky salt if desired. Serve with rye bread, challah, matzo, crackers, or crisp vegetable sticks such as cucumbers and celery.