Preheat oven to 400 degrees F (200 degrees C) and place rack in middle of oven. Line a cookie sheet with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda and salt. Cut the butter into small pieces and blend into the flour mixture with a pastry blender or two knives. The mixture should look like coarse crumbs. Stir in the chopped crystallized ginger and lemon zest. Add the buttermilk to the flour mixture and stir just until the dough comes together. Do not over mix the dough.
Transfer to a lightly floured surface and knead dough gently four or five times and then pat the dough into a circle that is about 7 inches (18 cm) round and about 11/2 inches (3.75 cm) thick. Cut this circle in half, then cut each half into 3 or 4 pie-shaped wedges (triangles). Place the scones on the baking sheet. Make an egg wash of one well-beaten egg mixed with 1 tablespoon milk and brush the tops of the scones with this mixture.
Bake for about 20 to 25 minutes or until golden brown and a toothpick inserted in the middle comes out clean. Remove from oven and then turn your broiler on high. Sift confectioners (powdered or icing) sugar heavily over the tops of the scones and place them under the broiler. Broil for just a few seconds, turning the pan as necessary, until the sugar has melted and turns golden brown. Make sure to watch the scones carefully as the sugar will burn very quickly. Transfer to a wire rack to cool.