Preheat the oven to 400 degrees F.
Unfold the thawed puff pastry sheets and lay them out on a flat, lightly floured surface. Use a knife to cut along the fold marks and then down the center to create 6 equal rectangles. Arrange the puff pastry squares on a parchment paper-lined baking sheet with at least 1" between each pastry.
Using a knife, lightly cut opposing corners but not all the way to the edges. (See process picture) With a fork, poke a few holes into the center of each pastry to allow the outside border to rise and puff up while the center stays lower and holds the filling.
In a medium sized saucepan, add the diced apples, butter, brown sugar, and cinnamon. Cook over medium heat for 4-5 minutes, or until the apples are fork tender.
Add about 2 tablespoons of apple filling to each puff pastry rectangle. Fold the 2 cut corners over the apple filling. (You can dip your finger in water and use that to help the puff pastry stay in place) Repeat the process and assemble all of the puff pastries.
Whisk together the egg and water in a small bowl, then use a pastry brush to brush all of the exposed areas of the puff pastry. Sprinkle a little coarse sugar on top of each pastry.
Bake in your preheated oven for 14-18 minutes, or until golden brown.
While they are baking, combine the powdered sugar, vanilla extract, and a tablespoon of milk into a small bowl. Mix well—the consistency should be somewhat thick, but still thin enough to drizzle. If the consistency is too thick, add a little more milk. If too thin, add more powdered sugar.
Once the danishes are baked, remove from the oven and cool on a wire rack for 10 minutes before drizzling the glaze over the tops. Enjoy!