In a large skillet, heat 1 tbsp of fat over medium-low heat. Add sliced onions and a pinch of salt. Cook slowly, stirring often, until caramelized and golden—about 15–20 minutes. Set aside.
Add another tablespoon of fat to the same skillet and increase heat to medium.
Season the chicken livers lightly with salt, pepper, and thyme. Add to the pan in a single layer. Cook for 2–3 minutes per side, until browned and cooked through but still tender. Do not overcook—they should be slightly pink inside.
Add garlic and caramelized onions back to the pan. Sauté everything together for 1–2 minutes.
Optional: deglaze with a splash of apple cider or balsamic vinegar for brightness.
Garnish with chopped parsley or sage before serving.