Sift flour, baking powder and 1/4 teaspoons salt into bowl. Cream butter and brown sugar with a mixer on medium speed until pale and fluffy, about 3 minutes. Add candied ginger, and beat for 2 minutes. Beat in egg and vanilla until well combined. Add flour mixture, then beat on medium-low speed until dough just comes together.
Shape dough into two 1-inch thick disks. Wrap tightly in plastic and refrigerate for at least 1 hour, or up to 3 days.
Preheat oven to 350°F Roll out 1 disk on a lightly floured surface to 1/4 inch thickness, and cut out 2-inch circles. Place rounds 1/2 inch apart on parchment-lined baking sheets. Rolls out scraps. Refrigerate rounds for 10 minutes.
Bake rotating sheets halfway through, until cookies are set and edges are bright gold, 12-14 minutes. Transfer parchment with cookies to wire racks. Let cook completely. Repeat with remaining dough. Cookies can be stored for up to 3 days.
Whisk confectioners' sugar, lemon zest and juice, honey, water, and pinch of salt in a bowl until smooth. Drizzle glaze over the cooked cookies. Let stand until glaze is set, at least 20 minutes. Glazed cookies can be stored overnight.