Step 1

Scones: Preheat oven to 350 degrees with rack in center.

Step 2

In a mixer fitted with the paddle attachment, beat together flour, granulated sugar, baking powder, baking soda, salt, crystallized ginger, ground ginger, and lemon zest. Add butter; beat on low speed until butter is somewhat broken down with some visible pieces remaining, about 30 seconds.

Step 3

In a liquid-measuring cup, whisk together buttermilk, cream, egg, and grated ginger. With mixer on low, add buttermilk mixture and beat until dough just comes together, 20 to 30 seconds (there will still be some flour mixture at bottom of bowl).

Step 4

Remove bowl from mixer. Using your hands, gather and lift dough, turning it over in the bowl, until remaining flour mixture has been incorporated into dough.

Step 5

Turn dough out onto a lightly floured surface and gently roll out 1 inch thick. Using a 2 1/2-inch round cutter, cut out 10 rounds, rerolling scraps as necessary. Transfer to a parchment-lined baking sheet, spacing about 2 inches apart.

Step 6

Bake until light golden brown, 30 to 35 minutes. Transfer sheet to a wire rack; let cool 10 minutes.

Step 7

Lemon Glaze: In a small bowl, whisk together confectioners' sugar and enough lemon juice to make a smooth, thick, pourable glaze. Brush glaze over warm scones and serve.