In a stand mixer fitted with the paddle attachment, combine all the dry ingredients on low speed. Slowly add the butter and beat until the mixture resembles coarse crumbs.
Add the eggs, one at a time, and beat on high speed 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. Refrigerate for 2 hours or up to 2 days.
Make the filling. Melt butter over medium heat in a large skillet. Add apples and saute for three minutes or until they begin to soften slightly.
Stir in cinnamon and brown sugar and cook 2 minutes more, until brown sugar has melted. Remove from heat an let cool completely.
Preheat the oven to 350 degrees.
Remove dough from refrigerator and roll one portion out to the thickness of about ⅛ of an inch on a surface that has been lightly dusted with sweet rice flour.
Using a toaster pastry shaped cookie cutter (or round 4½ inch diameter biscuit cutter), cut as many bottoms as possible, gathering and re-rolling out the dough a few times.
Place the pie bottoms on two cookie sheets and set aside. Repeat with remaining dough so you have the same number of bottoms and tops.
Place 1 tablespoon of pie filling on each pie bottom. Make an egg wash using 1 yolk and 1 tablespoon of water. Brush egg-wash around the edges of each pie using a pastry brush.
Place the top crust on each pie and use the tines of a fork to seal edges all around each pie. Sprinkle pies with granulated sugar, if desired.
Bake pies for 15-20 minutes or until golden brown. Remove from cookie sheet to a cooling rack to cool completely. Store in an airtight container at room temperature for up to 3 days.