Combine the blueberries in a medium-sized saucepan with apple juice. Bring to a simmer, then cover and simmer gently for 5 to 10 minutes, or until all the berries have softened and burst.
Dissolve the arrowroot powder in a small amount of cold water (1-2 tbsp). Stir slowly into the berry mixture and simmer for another minute or so, until it has thickened.
Stir in the maple syrup or your sweetener of choice. Add additional sweetener, to taste. Let the blueberry sauce cool to room temperature before serving.
Notes
This sauce can be made with other types of berries as well. Use small berries such as blueberries or raspberries whole. If using strawberries, remove hulls and chop strawberries into approximately ½-inch chunks.