In a medium saucepan over medium heat, combine ¾ cup water, sliced apples, brown sugar, white sugar, and cinnamon. Stir well and bring to a boil.
Once the apples are tender, add the butter and continue to cook for an additional 2 to 3 minutes.
In a small bowl, mix the cornstarch with the remaining ½ cup water until smooth. Whisk well to combine.
Add the cornstarch mixture to the apples to thicken. Stir continuously until the sauce thickens, then remove from heat.
