Preheat oven to 375°F (190°C).

In a large bowl, combine the softened butter and sugar.

Beat the mixture at medium speed until light and creamy.

Add the egg, 1 tablespoon of lemon zest, and 1/2 teaspoon of lime zest to the bowl.

Continue beating until all ingredients are well mixed.

In a separate bowl, whisk together the flour, chopped crystallized ginger, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, beating at low speed until just combined.

Shape the cookie dough into 1 1/4-inch balls using lightly floured hands.

Roll each ball in sugar to coat.

Place the sugared cookie dough balls 1 inch apart on ungreased cookie sheets.

Flatten each cookie to a 1 1/2-inch circle using the bottom of a glass dipped in sugar.

Bake the cookies for 7-10 minutes, or until the edges just begin to brown.

Remove from oven and let cool completely on the baking sheets.

In a small bowl, whisk together the powdered sugar, 1 teaspoon of lemon zest, 1/2 teaspoon of lime zest, and enough lemon juice to achieve your desired spreading consistency.

Once the cookies are cool, spread about 1 teaspoon of glaze over the top of each cookie.

Allow the glaze to set completely before serving.