In a large skillet, melt 2 tablespoons of butter over medium heat. Add the thinly sliced apples and cook, stirring occasionally, until the apples are soft and begin to release their juices—about 5 minutes. Be sure not to overcook the apples.

In a small bowl, whisk together ⅓ cup of brown sugar, 1 teaspoon of cornstarch, and 1 teaspoon of cinnamon. Stir this mixture into the apples and cook for another 3-5 minutes over medium heat until the apples are soft but still hold their shape. Remove from heat and set aside to cool.

Unfold the thawed puff pastry sheets on a flat surface. Cut along the fold marks to create three equal strips, then cut each strip in half to make a total of 12 rectangles.

Place the pastry rectangles on an ungreased cookie sheet, leaving about an inch of space between each one. Lightly score a border around each rectangle, about ½ inch from the edge, using a knife. Poke a few holes in the center with a fork to prevent puffing.

Spoon the cooled apple mixture onto the center of each pastry rectangle, making sure to avoid the outer scored border.

In a small bowl, whisk together 1 egg and 1 tablespoon of water. Use a pastry brush to apply a thin layer of the egg wash to the outer border of each pastry.

In a small bowl, combine 2 tablespoons of butter, 3 tablespoons of brown sugar, and ¼ cup of flour. Use a fork to mix until the mixture is crumbly. Sprinkle this topping evenly over the apples.

Preheat your oven to 400°F (200°C). Bake the pastries for 20 minutes, or until they are golden brown and puffed up. Remove from the oven and cool on a baking rack for 10 minutes.

To make the frosting, combine ½ cup of powdered sugar and 2-3 tablespoons of heavy cream in a small bowl. Stir until smooth, then drizzle over the cooled danishes. Enjoy your Apple Crumb Danishes!