Preheat oven to 400 degrees F. Line two large baking sheets with parchment paper and set aside.
In a mixing bowl, sift together flour, sugar, baking powder, baking soda, and salt. Cut in butter, using your fingers or a pastry cutter. Work the dough until mixture resembles a coarse meal.
In a small bowl, whisk together Greek yogurt, egg, and water. Add liquid ingredients to flour mixture, stirring until dough barely comes together. Dump the mixture on lightly floured counter and knead until the dough comes together. Don't overwork the dough.
Using a rolling pin, roll out the dough into a 1-inch thick circle. Cut into rounds using a biscuit cutter or cut into 2×2-inch squares. Combine dough scraps and roll out again to make remaining biscuits.
Place biscuits on prepared baking sheets and brush with the egg wash. Bake for 12-15 minutes. Serve warm with butter, honey, or jam!