These cookies get a hit of crunch, thanks to the coarse sugar coating. The secret ingredient? Shortening. It’s critical for creating that soft texture.
Arrange the racks in the top and bottom thirds of the oven; preheat to 350°. In a medium bowl, whisk the flour, pumpkin pie spice, baking soda, baking powder, and salt. In a large bowl, using an electric mixer on medium-high speed, beat the butter, shortening, and dark brown sugar until light and fluffy, about 2 minutes. Add the egg, molasses, and fresh ginger. Mix on medium until well blended. Add the dry ingredients. Mix on low until just blended.
Place the turbinado sugar in a medium bowl (or the empty flour bowl). Working in batches, form the dough into golf-ballsize balls and roll in the sugar to coat. Divide between 2 parchment paper–lined baking sheets, spacing 2 1/2 inches apart. Sprinkle with the crystallized ginger, gently pressing to adhere.
Bake the cookies, rotating and reversing the sheets halfway through, until the edges are firm but the centers are still soft, about 11 minutes. Let cool on the sheets for 3 minutes, then transfer to wire racks to cool completely.