Heat 2 tablespoons butter in a large skillet over medium heat. Add the green onions and cook until tender but not brown, about 5 minutes. Add the chicken livers, salt, and pepper, and cook, stirring occasionally, until no longer pink in the centers, about 7 minutes. Raise the heat, add the sherry, and cook until all theliquid has reduced and is syrupy, 3-4 minutes. Remove from heat and stir in the mustard, nutmeg, and cloves. Let cool for about 5 minutes.

Transfer the mixture to a food processor or blender and process until smooth, about 2 minutes. Add the remaining 4 tablespoons of softened butter, the cream cheese, and cognac, if using. Process until fully blended. Transfer the mixture to a serving bowl, cover with plastic wrap and refrigerate 12-24 hours. Garnish with chopped chives.