Place the Caramelized Onion Dip in a blender. Add the buttermilk, parsley, 1/2 teaspoon salt and some pepper and blend until smooth. Season with additional salt and pepper, if necessary.
Drizzle over the iceberg wedges. Serve immediately.
Heat the butter and olive oil in a heavy medium saucepan over medium-high heat. Add the onions and sugar. Cook, stirring constantly, until soft and golden brown, 15 to 20 minutes. Season with salt. Stir in the vinegar and simmer until the mixture is dry. Add the hot sauce if using. Remove the mixture from the heat and allow the onions to cool slightly.
Mix the cream cheese until smooth in a large bowl. Fold in the sour cream and caramelized onions. Season with salt and pepper. Garnish with chives if using. Can be eaten warm or transferred to the refrigerator to be eaten cold.