Preheat oven to 375°F. Line a cookie sheet with parchment paper or a silpat baking mat.
Place 1 tablespoon butter in a medium skillet. Heat over medium-low heat until butter is melted. Add the apple, granulated sugar, 3 tablespoons apple cider, and cinnamon. Stir to coat the apples. Cook until it bubbles, then cook for another 3 minutes. Stir cornstarch and water in a small glass or bowl. Pour into the apple mixture and cook until the mixture thickens. Remove pan from heat.
Unwrap thawed puff pastry sheet. Cut into 6 equal rectangles. Evenly divide the apples among the puff pastry rectangles and roll each up. Pinch the ends a little and pinch to seal. Place on prepared cookie sheet.
Bake for 15-18 minutes, until the croissants are golden brown. Let cool before glazing.
Make the glaze: melt remaining 1 tablespoon of butter in a small bowl. Whisk in powdered sugar and 1 tablespoon apple cider. Drizzle over croissants. Let set for a few minutes. These taste best the day they are made.