Preheat the oven to 350 degrees . Grease a 24-cup mini-muffin pan. In a bowl, combine the flour, baking powder, salt and ground ginger. Using a standing mixer, beat the granulated sugar and butter at medium speed for 1 minute. Beat in the whole eggs and egg yolk at medium speed. Stir in the dry ingredients on low speed.
Add 1 tablespoon batter to each muffin-pan cup and bake until a toothpick inserted in the centers comes out clean, 12 to 14 minutes. Let cool for 10 minutes; remove from the pan, then let cool completely.
In a small bowl, whisk together the confectioners' sugar, lemon juice and 1 tablespoon water. Dip the tops of the cakes in the glaze. Top with the candied ginger.