Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Combine almond flour, arrowroot, ginger, salt, cinnamon, and baking soda in a bowl. Add melted coconut oil, brown sugar, and molasses; mix well until a soft, sticky dough is formed. Wrap in plastic wrap and chill in the freezer for 40 minutes.
Roll out dough on a work surface dusted with arrowroot to 1/4 to 1/2-inch thickness. Dip cookie cutter in arrowroot, cut out cookies, and place on the prepared baking sheets.
Bake in the preheated oven until lightly golden, 8 to 10 minutes.