Allow puff pastry to thaw overnight in the refrigerator or for 30 minutes on the counter, or until easy to unfold.
Make apple filling
In a medium pot or deep skillet, melt butter over medium heat. As it melts, keep swirling the butter over the heat until it is light brown in color and smells nutty, about 3 to 5 minutes.
Immediately add the diced apples and stir around in the brown butter. Add brown sugar, cinnamon, nutmeg, allspice, and salt. Stir to combine. Cook, stirring occasionally, for about 10-12 minutes until the apples have slightly softened.
Whisk 1 tablespoon of cornstarch with 2 tablespoons of maple syrup and pour into apple mixture. Simmer for another 1 to 2 minutes or until mixture has thickened. Spread on a small sheet pan to cool.
Line 2 large sheet pans with parchment paper.
Roll one store-bought puff pastry sheet out to 11 inches per side. Use a pizza cutter or knife to divide into 4 equal pieces. Repeat with the second sheet of puff pastry. You will have 8 squares total.
Whisk together one egg with one tablespoon of water.
Assemble turnovers
Place one square of puff pastry on the counter in front of you like a diamond. Brush egg wash on the two sides facing you. Place 2 to 3 tablespoons of apples in the center of the square.
Fold the square over, corner to corner, to form a triangle, pressing the two edges together. Use the tines of a fork to seal the edges. Repeat with the remaining puff pastry squares. Place finished turnovers on a parchment lined baking sheet.
Place the first sheet pans of turnovers into the freezer to chill while you preheat the oven to 400°F. If you don’t have room for two sheet pans, make one tray of four turnovers and chill them while you make the second tray, then bake them separately.
Remove turnovers from the freezer and brush the tops with egg wash. Cut two one inch slits in the top of each turnover to release steam while baking.
Place into 400°F oven for 22 to 25 minutes, or until golden brown and puffed up. Cool on a wire rack at least 10 minutes. Make your glaze while they cool.
Make glaze
In a small bow, whisk together all of the glaze ingredients until fully combined. If you want it thinner, add another teaspoon or two of milk. If you want it thicker, add one or two more tablespoons of powdered sugar.
Drizzle over warm turnovers and let set for 15 minutes, or get sticky and dig right in!