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Preheat your oven to 400°F. Line a large baking sheet with parchment paper.
Prepare the apple filling: In a medium saucepan, melt 1 tablespoon of unsalted butter over medium heat. Add the diced apples, 1/4 cup of light brown sugar, 1/2 teaspoon of ground cinnamon, and 1/4 teaspoon of ground nutmeg. Cook, stirring occasionally, for 5 to 7 minutes, or until the apples are slightly softened. Stir in 1 tablespoon of lemon juice and 1 teaspoon of cornstarch. Cook for another 1 to 2 minutes, until the mixture thickens slightly. Remove from heat and let cool completely.
Prepare the crumble topping: In a medium bowl, combine 1/2 cup of all-purpose flour, 1/4 cup of granulated sugar, and 1/4 cup of old-fashioned rolled oats. Add 1/4 cup of cold unsalted butter pieces. Using your fingertips, a pastry blender, or a fork, cut the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces.
Unroll the thawed puff pastry sheet onto your prepared baking sheet. Using a sharp knife or pizza cutter, cut the pastry into 4 equal rectangles. For each rectangle, score a 1/2 inch border around the edge, being careful not to cut all the way through the pastry. This will help the edges puff up.
In a small bowl, whisk together 1 large egg and 1 teaspoon of water to create an egg wash. Brush the scored borders of each pastry rectangle with the egg wash.
Spoon an equal amount of the cooled apple filling into the center of each pastry rectangle, staying within the scored border. Sprinkle a generous amount of the crumble topping over the apple filling.
Bake the Danish pastries for 20 to 25 minutes, or until the pastry is puffed and golden brown, and the crumble topping is lightly browned and crisp. If the pastry edges brown too quickly, you can loosely tent them with aluminum foil.
While the Danish pastries are cooling, prepare the glaze: In a small bowl, whisk together 1/2 cup of confectioners' sugar, 1 tablespoon of milk, and 1/2 teaspoon of vanilla extract until smooth. If the glaze is too thick, add a few more drops of milk; if too thin, add a small amount of additional confectioners' sugar.
Once the Danish pastries have cooled for at least 15 minutes, drizzle the prepared glaze over them. Serve warm or at room temperature.

Preheat your oven to 400°F. Line a large baking sheet with parchment paper.
Prepare the apple filling: In a medium saucepan, melt 1 tablespoon of unsalted butter over medium heat. Add the diced apples, 1/4 cup of light brown sugar, 1/2 teaspoon of ground cinnamon, and 1/4 teaspoon of ground nutmeg. Cook, stirring occasionally, for 5 to 7 minutes, or until the apples are slightly softened. Stir in 1 tablespoon of lemon juice and 1 teaspoon of cornstarch. Cook for another 1 to 2 minutes, until the mixture thickens slightly. Remove from heat and let cool completely.
Prepare the crumble topping: In a medium bowl, combine 1/2 cup of all-purpose flour, 1/4 cup of granulated sugar, and 1/4 cup of old-fashioned rolled oats. Add 1/4 cup of cold unsalted butter pieces. Using your fingertips, a pastry blender, or a fork, cut the butter into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces.
Unroll the thawed puff pastry sheet onto your prepared baking sheet. Using a sharp knife or pizza cutter, cut the pastry into 4 equal rectangles. For each rectangle, score a 1/2 inch border around the edge, being careful not to cut all the way through the pastry. This will help the edges puff up.
In a small bowl, whisk together 1 large egg and 1 teaspoon of water to create an egg wash. Brush the scored borders of each pastry rectangle with the egg wash.
Spoon an equal amount of the cooled apple filling into the center of each pastry rectangle, staying within the scored border. Sprinkle a generous amount of the crumble topping over the apple filling.
Bake the Danish pastries for 20 to 25 minutes, or until the pastry is puffed and golden brown, and the crumble topping is lightly browned and crisp. If the pastry edges brown too quickly, you can loosely tent them with aluminum foil.
While the Danish pastries are cooling, prepare the glaze: In a small bowl, whisk together 1/2 cup of confectioners' sugar, 1 tablespoon of milk, and 1/2 teaspoon of vanilla extract until smooth. If the glaze is too thick, add a few more drops of milk; if too thin, add a small amount of additional confectioners' sugar.
Once the Danish pastries have cooled for at least 15 minutes, drizzle the prepared glaze over them. Serve warm or at room temperature.