Apple Dumplings

12 medium baking apples (Roman Beauty)
5 cups all-purpose flour, more as needed
Pinch of salt
1 pound butter, cut into pieces
Ice water as needed (~2 cups)
1 cup brn sugar
1 tsp cinnamon
1/8 tsp nutmeg
2 egg whites
Granulated sugar for sprinkling

Peel and core the apples. Combine half of the flour and salt in the container of a food processor; add 1/2 of the butter and process until blended. Add cold water as needed, pulsing only until the dough forms a ball. Wrap the ball in plastic and chill for 30 minutes. Repeat with remaining flour and the other 1 1/2 cubes of butter. Work in the butter with a pastry blender. Cream the remaining butter, brouwn sugar and cinnamon. Spoon a bit of this mixture into the cavity of each apple, using it all up. Preheat the oven to 375 degrees. Use as much flour as is necessary to roll one of the dough balls into a rectable about 12x18 inches. Place 6 of the apples on the dough, open side up. Cut the dough into 6 squares. Wet the edges of each square with a little ice water, then seal the dough by pulling each of the corners in turn onto the top of the apple; stretch the dough slightly to enclose the apple if necessary. Brush the pastry with egg white and sprinkle with sugar. Repeat with the remaining dough and apples. Place the apples on a baking sheet and bake until the pastry is brown and the apples are tender, about 30+ minutes. Let rest for at least 15 minutes, then serve warm with cinnamon or vanilla ice ream. Serves 12 or more.