Preheat oven to 450°F and line a baking sheet with parchment paper.
Mix together flours, sugar, baking powder, and salt in a large bowl. Grate the butter and stir into the dry ingredients.
Add the egg yolks to the milk and beat until well mixed, then stir into the dry ingredients. Do not over mix.
Fold cherries and walnuts into the dough, then turn out onto a floured surface. Knead a few times (dough should be somewhat sticky), then transfer to baking sheet and pat into a rectangle about 1/2-inch thick.
Using a bench knife or large chef's knife, cut dough into squares, but do not separate scones. Brush with egg whites.
Bake for 8-10 minutes, until golden brown.
Best eaten immediately, but can be stored for a day or two in an airtight container. Re-warm at 350°F for five minutes.