Peel and slice or chop the apples, and then place them in a large, microwave-safe bowl. (I use an inexpensive microwave popcorn popper with a vented lid. It’s handy for so many things besides popcorn–and great for that, too!)
Combine the sugar, cornstarch or arrowroot powder, and cinnamon in a small bowl. Sprinkle the mixture over the apples, and toss to thoroughly coat. Dot with the butter, and then cover the bowl and microwave on high for 10-12 minutes or until the apples are tender, stirring every 4-5 minutes. Check for doneness a little early and extend the cooking time if needed to account for differences among microwaves. The apples should be very tender but not mushy–sort of like apple pie filling.
Leftover apples may be cooled, covered, and refrigerated for up to one week. You may eat them cold or room temperature, although I like to reheat them gently in the microwave.