Preheat the oven to 350 degrees.
In a medium bowl combine the flour, baking soda, allspice, and salt. Set aside.
In a large bowl cream together the butter and sugar.
Add in the egg, lemon juice, lemon zest, and vanilla paste. Mix well.
Add the dry ingredients to the wet ingredients and mix until just combined.
Fold in the crystalized ginger.
Roll the dough into 1 inch balls or use a cookie scoop. Place on a baking sheet 2-3 inches apart.
Bake for 10-12 minutes or until lightly brown on the edges and the centers are set. I pressed down lightly in the center as soon as they came out.
Cool for 2-3 minutes on the baking sheet then transfer to a wire rack to finish cooling completely.
To make the glaze whisk together the powdered sugar, lemon juice, and ginger. Dip the tops of the cookies into the glaze then place on the wire rack. Let the excess drip off.
Allow the glaze to harden for 15 minutes before serving.