Prepare the crust. In a food processor fitted with the metal blade, combine all the dry ingredients on low speed. Slowly add the butter and pulse until the mixture resembles coarse crumbs.
Add the eggs, one at a time, and pulse until the mixture forms one solid lump.
Turn out onto a work surface, dusted with rice flour and knead 3 times. Divide in half, pat each half into a disk, and wrap well with plastic. Freeze for 30 minutes. (This recipe is enough for 2 bottom crusts. The second crust will keep for several months is wrapped tightly and sealed in a freezer bag).
Remove one disk from the freezer after it has chilled. Place a sheet of parchment on the counter and dust with sweet rice flour. Unwrap the dough and place on the flour. Dust the top of the dough with more flour and top with a second sheet of parchment. Roll the disk into a 10-inch round with a rolling pin. Remove one sheet of parchment and place the round into a standard pie plate dough side down. Remove the second sheet of parchment. Tuck any dough that’s overhanging the edges under and crimp the edge of the pie decoratively. Place the crust into the freezer to chill while you prepare the filling.
Preheat the oven to 375 degrees. Toss the prepared apples with the brown sugar, lemon juice, cinnamon, nutmeg and flour in a large bowl. Set aside.
Prepare the topping. Quickly wash & dry the food processor. To it add the flour, sugar, brown sugar and butter. Pulse until crumbs form.
Remove the prepared crust from the freezer. Pour the apple mixture into the crust. Gently press them into a dome shape. Using your hands, tightly pack the crumb mixture on top, completely covering the apples.
Place the pie on a parchment lined, rimmed baking sheet and bake for about 2 hours, or until the pie is lightly golden brown and the filling is bubbling. If necessary, tent the pie with foil if it is browning too quickly.