Line a good-quality baking sheet - preferably air-cushioned - with parchment paper for easier clean-up, or leave bare and ungreased.
When ready to bake, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 350F and preheat, lid closed, for 10 to 15 minutes.
Using a stand mixer or a hand mixer, beat the butter, shortening, and brown sugar in a mixing bowl until light and fluffy. Add the egg, molasses, and vanilla and beat until well-combined, scraping down the sides of the bowl as needed.
Add 1-3/4 cup of flour as well as the cinnamon, ground ginger, and salt. Try to roll a walnut-size ball between your palms. If the dough sticks to your hands and is too soft to roll, blend a bit more flour into the dough. Do not add too much, or your cookies will not spread properly and will toughen.
Roll the dough into balls, then give them a romp in a shallow bowl of coarse sugar. Arrange on the prepared baking sheet, then flatten each ball with the bottom of a drinking glass.
Bake the cookies for 7 minutes. Rap the baking sheet on the grill grate - this encourages chewier cookies - then rotate the pan 180. Continue baking for 5 to 7 minutes longer, or until the cookies are lightly browned. Let cool on the baking sheet for 1 to 2 minutes, then transfer to a wire cooling rack with a spatula. Bake the remaining cookies.
Store in an airtight container after the cookies have cooled completely.