Remove the puff pastry from the freezer and thaw according to the instructions on the package.
Once the puff pastry has thawed preheat the oven to 400 degrees.
In a medium sized pan melt the butter. Then, add in the diced apples and cook at medium heat until they soften. This should take about five to six minutes.
Reduce heat to low. Next add in the brown sugar, cinnamon, allspice, nutmeg, salt, and chopped pecans.
Let the mixture simmer for about four minutes or until the sugar and spices have carmelized the apples.
Remove from heat and set aside to cool.
Dust your counter with the flour. Roll out the first piece of puff pastry into a 10" square. Use a pizza cutter to divide the pastry into four smaller squares.
Place about a tablespoon of the cooled apple spice filling into the middle of a smaller square.
Whisk together the egg and water for the eggwash. Then use a brush to lightly coat the edges of the pastry with the eggwash to help seal the filling inside.
Bring the edges of the turnover together to form a triangle shape. Pinch the edges of the turnovers and crimp them with a fork.
Transfer each turnover to a parchment-lined baking sheet. Keep at least two inches in between each one.
With a knife, cut three small slits on the top of each turnover. Next, brush the whole pastry with the eggwash.
Bake for 20 minutes or until the pastry is a golden brown and puffed.
While the pastries are baking, whisk together the powdered sugar, heavy whipping cream, and the maple syrup.
Once the turnovers are done baking and are still warm, drizzle the maple glaze on the top.