Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
To make the oat flour, place the oats in a food processor and process until finely ground, about 1 minute. Pour into a bowl and scoop 1 cup oat flour back into the processor. Reserve any remaining flour for another use.
Add the whole wheat pastry flour, sugar, baking powder, ground ginger and salt to the processor. Pulse briefly to combine.
Add the chilled butter to the processor and pulse until the mixture is pale yellow and the consistency of a fine meal.
In a medium bowl, whisk together ½ cup non-fat milk, vanilla extract and egg white. Pour the mixture, along with the lemon zest, into the processor and pulse quickly until just mixed.
Turn the mixture out onto a generously floured surface. Sprinkle the dried cherries over the dough. Lightly dust your hands with flour and gently knead to mix in the dried cherries, and form the dough into a ball.
Transfer the dough to the prepared baking sheet. With lightly floured hands, form the dough into an 8-inch circle.
Cut the circle into 12 triangles, keeping the circle of dough intact.
Using 2 teaspoons of non-fat milk, lightly brush the tops of the scones. Sprinkle the turbinado sugar over top.
Bake for 16-20 minutes, or until the surface of the scones are golden brown. Cool on the tray or on a cooling rack. Cut the scones apart and serve.