Sift together the flour, baking powder, sugar, Matcha powder and salt.
Cut the butter into small pieces and mix into the flour with your hands until you get a coarse crumbly texture. Gently stir in the cherries.
Beat the milk and egg yolk, and mix it into the flour mixture until just combined.
Knead very lightly until the dough just comes together. Pat the dough down with your hands to 1.5 inch thickness. Using a 2.5 inch cookie cutter, cut into 8 circles.
Bake in a preheated oven at 400°F for 12- 15 minutes or until a toothpick comes out clean. Cool for 10 minutes on a rack.
Whisk the powdered sugar and milk until homogeneous. Use a spoon or a pipping bag to glaze the scones as desired.