In a large mixing bowl, combine the flour and salt. Add the cubed butter and using a pastry blender or a fork, cut the butter into the flour mixture until it is crumbly and no large chunks of butter remain. Sprinkle the vinegar over the flour mixture evenly. Then gradually add the milk to the mixture, stirring with a fork until it the dough forms a ball. (It might not require quite all the milk.) Cover the dough and refrigerate for at least 20 minutes or until the dough is easily handleable.
In another bowl, combine the brown sugar, flour, cinnamon, and butter, with a fork until the butter is well blended in and the mixture is crumbly.
Core the apples and slice into rings about 1/2-2/3 an inch thick. Remove the peel from the apple rings.
Remove the dough to a floured work surface and cut into 16 equal pieces. Dusting each with flour, roll the pieces out into 5-6 inch circles.
Heat oven to 375 degrees.
Place one apple ring onto each circle of dough. Top each apple ring with 2 teaspoons of the cinnamon sugar mixture. Fold the edges of the dough over the apples, leaving the centers open.
Place one inch apart on an ungreased baking sheet.
Brush the outside edges of the pastry dough with the melted butter and sprinkle over it the white sugar.
Bake at 375 degrees for 30-35 minutes or until golden brown and the apples are tender.