Prepare the livers – Rinse them under cold water, pat dry, and remove any tough bits. Cut into bite-sized pieces.
Sauté the onions – Heat olive oil and 1 tbsp butter in a pan over medium heat. Add the onions and cook until soft and golden, about 5 minutes. Stir in the garlic and thyme.
Cook the livers – Push the onions to the side of the pan. Add the chicken livers and sear for about 2-3 minutes per side. They should be browned on the outside but slightly pink inside.
Season and deglaze – Sprinkle with salt and pepper. Pour in balsamic vinegar (or lemon juice) and chicken broth if using. Stir everything together and let cook for another minute.
Finish with butter – Stir in the remaining butter for extra richness. Take it off the heat and let it sit for a few minutes..
Garnish and serve – Sprinkle with fresh parsley and serve warm with crusty bread, mashed potatoes, or rice.