Line 2 rimmed baking sheets (half sheet size) with parchment paper.
In a medium bowl, whisk together the flour (2 1/4 cups), ginger (2 3/4 teaspoons), baking soda (1 teaspoon), and salt (1/4 teaspoon); set aside
In a large mixing bowl, using a handheld electric mixer on medium-high speed, cream together butter (3/4 cup) and 1 cup of sugar until well blended. Add the egg (1), molasses (1/4 cup), and crystallized ginger (3 tablespoons), and combine. Gradually add the flour mixture and beat on low, scraping down the sides of your bowl occasionally to incorporate everything.
Pour remaining sugar (1/3 cup) into a shallow bowl. Use a leveled-off medium cookie scoop to shape the cookies, then roll them in the sugar to coat each side. Place them 2" apart on prepared baking sheets.
Place baking sheets in the fridge for 30 minutes. Position your oven racks, so one is in the center of the oven, and preheat the oven to 350°F.
Bake chilled cookies in the oven for 6 minutes. Rotate the pan, and bake for an additional 6-8 minutes. You'll know the cookies are done once the surface is cracked, and the top of the cookies feels dry to the touch. After 5 minutes on the cookie sheet, transfer cookies to a cooling rack. Enjoy!