Whisk the flour, baking soda, ginger, allspice, and salt together in a medium bowl. Set aside.

In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, beat the butter and granulated sugar together on medium-high speed until creamed, about 3 minutes. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) Add the egg, lemon juice, lemon zest, and vanilla extract and beat on high speed until combined, about 1 minute. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine.

Add the dry ingredients to the wet ingredients and mix on low until combined. Beat in 2 Tablespoons of chopped crystallized ginger. Dough will be thick and sticky. Scoop small sections of dough (about 1 scant Tablespoon of dough each) and roll into balls. Very lightly dip the tops of each into remaining crystallized ginger. (You don’t want too much—just a few pieces.) Place dough balls onto a large plate or lined baking sheet.

Cover and chill the cookie dough balls in the refrigerator for at least 1 hour (and up to 4 days).

Preheat oven to 350°F (177°C). Line baking sheets with parchment paper or silicone baking mats. Set aside.

Arrange chilled cookie dough balls 3 inches apart on the baking sheets. Bake for 11-13 minutes or until lightly browned on the sides. The centers will look very soft.

Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Whisk the glaze ingredients together. If desired, add more confectioners’ sugar to thicken or more juice to thin out. The thicker the glaze, the whiter (and less translucent) it will be. Drizzle on cooled cookies. Icing will set after about 1 hour, so these are convenient to store and transport.

Cookies without glaze stay fresh covered at room temperature for up to 1 week. Cookies with glaze stay fresh covered at room temperature for up to 3 days or in the refrigerator for up to 1 week.