Heat oven to 400 degrees F. Grease a 9-inch pie pan.
In a food processor, mix sorghum blend, tapioca flour, rice flour, 2 tablespoons
sugar, gum, salt, baking soda and shortening. Process until it forms loose crumbs.
Add the milk and vinegar, pulsing until dough forms a ball. Remove the dough and
knead it until smooth, then shape into two disks, wrap with plastic wrap and chill
for an hour.
Place disk between 2 pieces of flour dusted plastic wrap and roll in into a 10-inch
circle. Transfer the dough to the pie pan and press to fit the pan, crimping edges.
Brush edges with egg white.
Filling: Add the lemon juice to a bowl. Peel and core the apples and slice them.
Toss the apple pieces in the juice. Add cornstarch, cinnamon and sugar, stirring.
Topping: Blend all ingredients except butter in a food processor. Add butter
until mixture resembles wet sand. Toss filling and pour into crust. Place topping
over and around apples.
Place pie on baking sheet and bake 9 minutes.
Reduce heat to 350 degrees F and continue baking until apples in center are tender
and filling is bubbling, 50 minutes.