Using an electric mixer, beat the butter then add in icing sugar, and beat until light and fluffy. Beat in half a teaspoon of the lemon zest, the ground ginger, the crystallized ginger, and salt.
Add the flour in 1/4 cup at a time, beating after each addition. Spread the crust mixture evenly over the bottom of a 13x9-inch baking dish. Bake at 350°F for 12 to 15 minutes, or until browned lightly around the edges.
In another bowl, beat all the topping ingredients together until well blended.
Remove the crust from the oven and pour the lemon batter over. Return to oven and bake for another 15 to 20 minutes or until the top is golden.
If you want, sift a little additional powdered sugar over the top.
Once cool, dust with additional icing sugar.