Preheat oven to 400 degrees F. Unfold pastry sheet, roll out to thin a little. Cut sheet into four squares (I use a pizza cutter for this). Place squares on a parchment or silicone-lined baking sheet.
Melt plant butter in a medium/large skillet over medium heat. Add apples, cook and stir for about 2 minutes. Add brown sugar, cinnamon, nutmeg, small pinch of salt and optional lemon juice. Cook and stir for about 2 more minutes.
Meanwhile, stir together cornstarch and water or apple juice. Pour into the skillet and mix well, cooking for another minute or until the mixture has thickened. Remove from heat to cool slightly.
Spoon apple mixture into the center of each pastry square. Fold over from corner to corner to form a triangle shape, and press edges to seal (I use a fork to press them firmly). Make sure there is about 1 inch of space between pastries on baking sheet.
Bake for 18-20 minutes, or until turnovers are puffed and lightly browned. Cool completely before glazing.
Glaze: Mix together the confectioners' sugar, milk or lemon juice and vanilla in a small bowl until it's a thick but pourable consistency. Adjust the thickness by adding more sugar or milk/juice if necessary. Drizzle glaze over the cooled turnovers. Enjoy!