In a large bowl, cream the butter and granulated sugar together with an electric mixer on medium-high speed until light and smooth, about 2 to 3 minutes.
Add the egg and mix until fully incorporated. Add the molasses and mix until combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, and ground ginger.
Add the dry ingredients to the wet ingredients and mix just until combined.
Cover the dough and refrigerate for 45 to 60 minutes, until firm enough to scoop.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper, if desired.
Scoop the dough into balls approximately 2 tablespoons in size. Roll each ball evenly in powdered sugar.
Place the dough balls on the prepared baking sheet, spacing them about 2½ inches apart.
Bake for 11 to 12 minutes, until the edges are set and the tops are cracked. The centers should remain soft.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.