Add apple juice, vinegar, ketchup, and 1/4 cup of brown sugar to a small saucepan. Bring to a simmer over medium heat. Stir often. Add mustard, black pepper, cayenne pepper, reduce heat and simmer over low heat for 3-4 minutes.
Give the sauce a taste. If you need to up the sugar, add 1 1/2 to 2 tablespoons or more to achieve the desired sweetness. Let the sauce simmer for an additional 3 minutes. Remove from heat and stir in butter.
Let the sauce cool for about 15 minutes before using. If making ahead of time, let it cool for 30 minutes, then transfer to an airtight container. Store in the refrigerator for up to 1 week after preparation. Rewarm to room temperature before using.
*You do not need to use mustard for this recipe. I include it to add a little depth to the sauce. You can certainly omit it.
Use this sauce on pulled pork or pulled chicken.