Heat 2 tbsp schmaltz in a skillet over medium heat. Add onions and cook 12–15 minutes, stirring occasionally, until deeply caramelized. Remove and set aside.
Add remaining schmaltz to the skillet and sear chicken livers 4–5 minutes per side, until cooked through but not dry.
Combine livers, onions, and chopped eggs in a food processor.
Pulse until well combined but still slightly coarse — avoid processing into a completely smooth paste.