Preheat the oven to 400 F.
I like to use the food processor to mix up pie crust but you could use the traditional pastry cutter or two knives as well. Mix together the flour and salt, then mix in the butter until crumbly. Add the ice water a spoonful at a time until the dough barely sticks together. Set aside while you deal with the apples.
Peel and chop the apples, then mix with the sugar, tapioca, cinnamon, nutmeg and melted butter.
Roll the pie crust out to 1/4" thickness and cut into circles the size you'd like. If you opt for larger 6" circles, you'll get about 6 turnovers. Use a bowl or plate to cut out the circles, inverting it onto the crust and cutting around the edge.
Put some apple filling into the middle and fold the pastry over to form a half circle, pinching the edges together. Place on a cookie sheet. Repeat until the dough is all gone. Cut small slits in the turnovers to let the steam escape.
Bake at 400 for 15 minutes, then turn the heat down to 350 and bake another 30 minutes or so. Cool on a wire rack.