In a medium size bowl, toss together the flour, ginger, cinnamon, salt, and baking soda. Set aside.
In a large bowl with a hand mixer or the bowl of a stand mixer fitted with the paddle attachment, blend the melted butter and molasses together until fully incorporated. Add the brown sugar and beat again until combined. Beat in the egg. Scrape down the sides of the bowl with a spatula as necessary.
Reduce mixer speed to low and gradually add flour mixture. Mix until just combined. Cover bowl and chill in the refrigerator at least 1 hour and up to 3 days. If chilling longer than 1 hour, allow to sit at room temperature about 15 minutes before rolling into balls.
When you are ready to bake the cookies, preheat the oven to 350ºF. Line a baking sheet with parchment paper or a silicone baking mat. Set aside.
Pour the powdered sugar onto a large plate. Using a large cookie scoop, scoop the dough out of the bowl and roll into a ball with your hands. Dough ball does not need to be perfect. Roll the ball of dough generously in the powdered sugar. Place no more than 8 balls of dough on a baking sheet at one time (4 rows of 2). Chill dough you are not using.
Bake cookies for 15-16 minutes or until cookies look mostly matte (not wet or shiny). Remove from oven and cool on the baking sheet for 3 minutes before transferring to cooling rack to cool completely. Store cookies in an airtight container at room temperature up to 10 days. Baked cookies freeze well, up to 2 months. Rolled cookie dough can be frozen up to 3 months. Roll in powdered sugar before baking and bake frozen. Add another 1-2 minutes to baking time.