Wash the apples very well, then cut the sides off to remove the cores. Add the apple pieces to a medium pot that has approximately an inch of water in it and place over high heat. Cook the apples for 10 minutes until tender and cooked through. Turn the heat off, then cover the pot and allow to cool for another 10 minutes before pureeing until smooth in a blender.
If you have a food mill, the apples can be cooked whole and then processed through the mill, increasing your yield.