Preheat the oven to 350 degrees F. Line an 8-by-8-inch baking pan with parchment.
In a stand mixer fitted with the paddle attachment, beat the coconut oil with both sugars on medium-high speed until light and fluffy.
Mix in the egg, molasses and vanilla on medium speed until incorporated, scraping down the bowl as needed.
Add the salt, baking powder, ground ginger, cinnamon, allspice, all the flours and tapioca starch. Mix on low speed just until combined and no flour streaks remain. Stir in the candied ginger and chocolate chips with a rubber spatula.
Transfer the batter to the prepared baking pan and press into an even layer.
Bake until golden brown around edges and a toothpick inserted in the middle comes out clean, 30 to 35 minutes.
Let cool completely in the pan, then remove, peel off the parchment and cut into squares or rectangles.