Place the chicken livers on paper towels to drain. Place the eggs in your food processor bowl.
Heat 2 tablespoons of the olive oil over medium heat in a large skillet. Add the chopped onion and fry until golden, stirring occasionally, about 10 minutes. Add the garlic and cook a few more seconds, just until no longer raw. Using a spatula, transfer the skillet contents, including any remaining oil, to the food processor.
Add 2 more tablespoons oil to the skillet. Add the chicken livers and fry over medium heat until brown on the outside but still pink on the inside, 2-3 minutes per side. Don’t overcook, or the livers will become dry.
Again, use the spatula to transfer the skillet contents, including the livers, the oil and any tasty bits left on the bottom of the skillet, to the food processor. Add the salt and pepper. Pulse just until smooth, about 30 seconds, stopping once to scrape the sides with a spatula.
Transfer the chopped liver to a serving dish. Cover and keep in the fridge for at least two hours, allowing flavors to meld. Don’t eat chopped liver when still warm! It needs time to develop its deep, earthy flavor.