Preheat oven to 400 degrees Fahrenheit or 200 degrees Celsius.
Peel apples and chop into ¼ inch pieces.
Combine with 1 T. butter and 1 T. sugar in a medium saucepan. Cook over medium-high heat, stirring occasionally, for 15 minutes. Apples should be entirely tender but still intact. Let cool.
Meanwhile, combine cinnamon with remaining ¼ c. sugar.
Roll puff pastry into a 30 x 24 cm (12 x 9.5 inch) rectangle.
Place pastry on cutting board. Spread with softened butter.
Sprinkle with half of the cinnamon-sugar mixture, then spread cooked apples evenly across the pastry.
Sprinkle with remaining cinnamon-sugar mixture.
Roll into a jelly roll shape, starting with one of the shorter ends. Place roll in the refrigerator for 15 minutes to give the pastry dough time to firm up.
Cut into 1-inch slices. Assemble on parchment paper-lined baking sheet with at least an inch of space between each one.
Bake for 25 minutes, then check whether pastry is cooked through and golden brown. If not, bake for another 5 minutes.
Let cool on baking rack for 5 minutes.
While rolls are baking, stir together powdered sugar and milk in a small bowl to create a glaze.
Drizzle on apple cinnamon rolls, then serve.
