In a large bowl, stir the lemon juice into the diced apples.
2 cups apples, peeled and diced (about 4 medium apples), 1 ½ teaspoons lemon juice
In a large skillet, over medium heat, cook the butter until golden brown. Add the apples, brown sugar, granulated sugar, cornstarch, cinnamon, nutmeg, salt, and cloves and stir to combine.
2 tablespoons unsalted butter, ½ cup light brown sugar, packed, 2 tablespoons granulated sugar, 2 teaspoons cornstarch, ¾ teaspoon cinnamon, ¼ teaspoon nutmeg, ⅛ teaspoon fine sea salt, ⅛ teaspoon cloves
Cook the apple mixture until the apples have softened and tender and the liquid has thickened.
Stir in the vanilla. Cool the apple filling for 15 minutes at room temperature. Refrigerate for an additional 30-45 minutes until cold.
1 teaspoon vanilla extract
When the apples have chilled, preheat the oven to 400F and line two baking sheets with parchment paper.
Working with one pastry sheet at a time, roll out the cold, thawed puff pastry sheets out on a lightly floured surface into a 12-inch square. Cut each sheet into 4 equal squares. Repeat with the second sheet of puff pastry to make 8 squares total.
2 sheets frozen puff pastry, thawed
Divide the chilled apple filling among the pastry squares (a few tablespoons each), concentrating the apple filling to one corner and leaving a ½" border around the perimeter of the pastry.
Whisk together the egg with the water.
1 large egg, 1 teaspoon water
Using a pastry brush, light brush the edges of the pastry with egg wash.
Fold one point of the puff pastry over the apple filling to the opposite point, creating a triangle. Crimp and seal the turnovers by pressing the tines of a fork along the two straight sides.
Brush the tops with egg wash and sprinkle with raw or turbinado sugar.
1 tablespoon raw or turbinado sugar
Bake the turnovers to golden brown, about 18-20 minutes. Cool completely.
While the turnovers cool, whisk together the confectioners sugar, cream and vanilla until smooth and creamy. Drizzle icing over cooled turnovers and serve.
¾ cups confectioners sugar, 1 - 2 tablespoons heavy cream, or milk, ¼ teaspoon vanilla extract