Preheat oven to 375°F. Put dry mix into large mixing bowl. Add butter and cut in with pastry blender, fork, or two knives until it resembles coarse crumbs.
In a small bowl, whisk together egg and ¼ cup milk. Add liquid to flour and butter, and stir with a spoon lightly until mixture holds together in a ball. Do not over work dough.
Gently turn dough onto a well-floured work surface. Knead gently until it holds together. Form dough into 8" x ½" round. Cut round into eight wedges. Brush top of each scone with milk wash and place on baking sheet 1-½" apart.
Bake until lightly browned, approximately 12-15 minutes. Allow scones to cool on a wire rack for about ten minutes.
In a medium bowl, whisk together water, powdered sugar, and coffee, and continue to whisk until glaze is smooth. Drizzle over cooled scones.