Combine the melted butter, molasses, applesauce, brown sugar, and grated ginger in a medium sized bowl. Whisk until smooth. In a separate bowl or the bowl of a stand mixer, whisk together the flours, baking soda, spices, and salt. Add the wet ingredients to the dry, then mix until the dough comes together and you no longer see pockets of dry flour. It will be a fairly soft dough. Cover the bowl and chill the dough for at least 2 hours.

Preheat the oven to 350 degrees and line two baking sheets with parchment paper or silicone mats. Remove the chilled dough from the fridge and put the turbinado sugar in a shallow bowl. Using a 0.5-ounce cookie scoop or tablespoon measure, scoop up portions of the dough, roll them into a ball, then drop them into the sugar. Roll the ball of dough around until it is coated in sugar. Place the cookies on your prepared baking sheet at least one inch apart. Bake the cookies for 13-15 minutes or until just set. If you prefer a more crisp cookie, bake them for 16-18 minutes.

Transfer the cookies to a rack to cool. Cookies can be enjoyed warm or at room temperature.