Sautéing Chicken Livers: In a large skillet over medium heat, melt the butter. Add the chicken livers and sauté until they are browned on the outside but still slightly pink in the middle, about 3-4 minutes per side. Season with salt and optional black pepper during cooking.
Blending: Transfer the sautéed chicken livers to a blender, along with 1 cup (about 240 ml) of chicken broth. Blend until smooth.
Combining: Pour the liver mixture back into the skillet or a soup pot. Add the remaining 3 cups (about 710 ml) of chicken broth and bring the mixture to a simmer over medium heat, stirring constantly.
Adding Cream: Once the soup reaches a simmer, reduce the heat to low and stir in the heavy cream. Warm through, ensuring not to boil, to keep the cream from curdling.
Final Seasoning: Taste the soup and adjust the seasoning with additional salt and pepper if needed.
Serving: Serve the soup hot, optionally garnished with a sprinkle of fresh herbs like parsley or chives for color and flavor.