Combine warm water with sugar, stirring until sugar is almost dissolved. Add yeast, stirring until incorporated.
Cover bowl with plastic wrap. Set aside in a warm place for 10 minutes, or until foamy.
In a very large mixing bowl (stand mixer if you have it!), combine flours, starches, xanthan gum, and salt, whisking until well combined.
Whisk egg into yeast mixture, add to the dry ingredients and stir until well combined. Slowly add milk , mixing well to combine.
Pour olive oil into a large clean bowl, swirl to coat the bottom and sides of the bowl.
Transfer dough to oiled bowl, flip to coat in oil. Loosely cover with plastic wrap, allow to rise in a warm place for an hour or two.
Preheat oven to 450 F (230 C), line two large cookie sheets with parchment paper.
Divide dough into 5 equal sized portions. Roll into rounds about 6-8" across.
Transfer pita rounds to each cookie sheet, spaced apart.
Bake for 6-7 minutes, until puffy and golden.
Flip over and bake for 2-3 more minutes.
Serve right away (Cut in half, then slit open with a sharp knife to make pockets!), or store in plastic baggies for up to a few days (fresh), or freeze for up to 3 weeks.