Position an oven rack in the center of the oven; preheat to 350°.
Using a stand mixer fitted with the paddle attachment, mix together the flour, baking powder, baking soda, salt, sugar, ground ginger, crystallized ginger, and lemon zest on low speed for 10-15 seconds, or until combined.
Scatter the butter over the top and beat on low speed for about 30 seconds, or until the butter is somewhat broken down and grape-size pieces are still visible.
In a small bowl, whisk together the buttermilk, cream, egg, and grated ginger until thoroughly mixed.
On low speed, pour the buttermilk mixture into the flour-butter mixture and beat for 20-30 seconds, or just until the dough comes together.
There will still be a little loose flour mixture at the bottom of the bowl.
Remove the bowl from the mixer stand.
Gather and lift the dough with your hands and turn it over in the bowl, so that is starts to pick up the loose flour at the bottom.
Turn over the dough several times until all of the loose flour is mixed inches.
Dump the dough onto a lightly floured work surface and gently roll it out about 1 inch thick.
Using a 3 1/2 inch round cookie cutter, cut out circles.
Reroll scrapes and cut out more circles; you should have 10 circles.
Place them on a baking sheet, spacing them 2-3 inches apart.
Bake for 40-45 minutes, or until the scones are a light golden brown on top.
Transfer to a wire rack to cool for 10-15 minutes.
Lemon Glaze-while the scones are cooking, in a small bowl, whisk together the powdered sugar and enough lemon juice to make a smooth, thick pourable glaze; you should have about 1/2 cup.
When the scones have cooled 10-15 minutes, brush the tops evenly with the lemon glaze, then serve.
The scones taste best on the day they are baked, but they can be stored in an airtight container at room temperature for up to 3 days. If you keep them longer than 1 day, refresh them in a 300 degree oven for 4-5 minutes.