Preheat the oven to 400F and line a large baking sheet with parchment paper.
Next, heat a skillet on medium heat and add butter. Once the butter is melted, add the diced apples and lemon juice. Cook the apples for about 3 minutes. Then, add the brown sugar, cinnamon, and cardamon, and cook for an additional 3 minutes or until the apples are softened.
In a small bowl, mix cornstarch and cold water to make a slurry. Once thoroughly combined, pour the slurry into the apples and cook for an additional 1-2 minute to thicken. Remove from heat and place the apples in a heat-safe bowl and let the apple filling cool for about 20 minutes.
Next, unwrap the thawed pastry dough. Then, roll the dough on a floured surface horizontally and vertically to smooth out the seams and get the sheets to resemble a square. Then, using a sharp knife or pizza cutter, cut each pastry sheets into 4 equal squares.
Step 5. In a medium bowl, beat the egg and water together to make the egg wash. Next, fill each square with about 2-3 tbsp of the cooled apple filling, but be sure to leave room along the edges, as the pastry will need to close. Then, with a pastry brush, brush the egg wash along the sides of the pastry square (this will limit the amount of apple filling that may sip from the dough).
Next, bring two corners of the square pastry together so the sides align. Using a fork, crimp all sides of the pastry, which should now look like a triangle. Repeat this step until all the turnovers are made. Then, carefully transfer the turnovers to the prepared parchment paper and brush the tops of each turnover with egg wash. The turnovers should be at least 1 inch apart.
In the preheated oven, bake the apple turnovers on the center rack for 20-23 minutes or until perfectly golden brown. Once done, take them out of the oven to cool.
Next, whisk together the sifted powdered sugar, heavy cream, and vanilla extract. Monitor the amount of heavy cream you use to ensure you get the consistency you want. Once your apple turnovers have slightly cooled (about 5-10 minutes), drizzle the glaze onto the apple turnovers and enjoy while they are fresh!