Microwave the coconut oil in a large microwave-safe bowl until melted, 1 to 2 minutes. Whisk in the granulated sugar and molasses. The mixture should be mostly smooth; if it?s not, return to the microwave for 30 to 45 seconds and whisk again to combine. Set aside to cool slightly.
Whisk the flour, pie spice, ginger, baking soda and salt in a medium bowl. Whisk the flour mixture into the coconut oil mixture until smooth, switching to a rubber spatula when the dough becomes too stiff to whisk (it will seem dry at first, but will come together).
Scrape the dough onto a large piece of plastic wrap and roll into an 8- to 9-inch-long log. Wrap in the plastic wrap. Press the sides with a ruler to square off the log. Refrigerate, re-pressing the squared sides after about 20 minutes, until the dough is firm, at least 1 hour or overnight.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Unwrap the dough and slice 1/4 inch thick. Arrange the slices about 1 inch apart on the prepared pans.
Bake, switching the pans halfway through, until the cookies are firm around the edges, 18 to 22 minutes. Let cool completely on the pans.
Make the glaze: Whisk the confectioners' sugar and 2 teaspoons water in a small bowl. Gradually stir in up to 2 more teaspoons water until the glaze is smooth and thick. Dip half of each cookie in the glaze; return to the baking sheet and sprinkle with coarse sugar. Let set, about 30 minutes.