Cook the apples, cranberries, brown sugar, cinnamon, nutmeg, lemon juice, and vanilla in a large skillet over medium heat for 6 to 8 minutes, stirring occasionally, until the apples begin to soften and the cranberries start to burst.
2 medium Honeycrisp or Granny Smith apples, 1 cup cranberries, ½ cup light brown sugar, 1 teaspoon ground cinnamon, ⅛ teaspoon ground nutmeg, 2 teaspoons lemon juice, 1 teaspoon vanilla extract
Stir together the cornstarch and water, then add the mixture to the fruit. Cook for 1 more minute, stirring constantly, until the filling thickens. Transfer the filling to a bowl and let it cool completely.
1 tablespoon cornstarch, 1 tablespoon water
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Whisk together the egg and 1 tablespoon of water to make an egg wash.
1 large egg, 1 tablespoon water
Unfold the puff pastry sheets and cut each sheet into four equal squares.
1 package frozen puff pastry
Spoon about 2 tablespoons of the cooled filling into the center of each pastry square.
Brush the edges with the egg wash, fold the pastry diagonally into triangles, and press the edges together with a fork to seal.
Cut two or three small slits in the top of each turnover to vent the steam.
Brush the tops with the remaining egg wash and sprinkle with coarse sanding sugar, if using.
Coarse sanding sugar
Bake for 20 to 24 minutes, or until the turnovers are puffed and deep golden brown.
Let cool for about 10 minutes.
Whisk together the powdered sugar, milk, and vanilla until smooth, then drizzle over the warm turnovers.
1 cup powdered sugar, 2 tablespoons milk or cream, 1 teaspoon vanilla extract