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Defrost frozen puff pastry, if it's not defrosted already. It's easiest to let it sit out on your countertop for 40 minutes. Preheat oven to 400u00b0 F. Melt butter (or substitute) in a large skillet over medium-high heat. Cook the diced apples for 2 minutes, stirring occasionally. Juice the 1/2 lemon over the apples and add coconut sugar, arrowroot, cinnamon, nutmeg, ginger, and lemon zest. Cook for 3 minutes, until apples are knife-tender and sauce is thickened. Remove from heat stir in the vanilla or almond extract. While filling cools, unfold the puff pastry on a lightly floured surface. With a sharp knife, cut it into 4 equal squares for 4 large apple turnovers. (This can also be cut into 8 equal squares for 8 small turnovers.) To assemble, brush the egg wash or almond milk along the edges. This will be a binder for the turnovers. Add 1/4 (or 1/8 if you're making smaller turnovers) of the spiced apple mixture in the middle of each square. Fold pastry in half diagonally and lightly press together. Run a knife along the edges to seal the pastries completely and create a decorative design. Transfer to baking sheet lined with a silpat or parchment paper. Make 1 or 2 small slits on the top of each turnover and sprinkle with additional sugar if desired. Bake for 15 to 18 minutes until top is golden brown. Remove from oven and, this is important!!, let cool for 10 minutes on a wire rack. For the glaze: Whisk all of the ingredients together until combined. Add more milk to make the glaze thinner, or more powdered sugar for a thicker glaze. Drizzle it over warm turnovers and serve immediately.
