In a large bowl, whisk together the flours, baking soda, ground ginger, cinnamon, black pepper, cayenne, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and brown sugar on medium-high speed until fluffy, 1 to 2 minutes. Add the egg yolk and beat until incorporated, 1 minute. Add the molasses and grated ginger and beat until just combined. Reduce the speed to medium, slowly add the flour mixture, and beat until just incorporated. Cover the bowl with plastic wrap and refrigerate until firm, 1 hour.
Preheat the oven to 300°F. Line two baking sheets with parchment paper.
Place the turbinado sugar in a shallow baking dish. Using a spoon, portion out 1 tablespoon of the dough at a time and roll into round balls. Roll the balls in the turbinado sugar to coat, pressing gently to adhere the sugar to the balls. Place on the prepared baking sheets 2 inches apart and bake until browned around the edges but still slightly soft in the center, 24 to 25 minutes. Cool on the baking sheets for 5 minutes, then use a wide metal spatula to transfer the cookies to a wire rack to cool completely. The cookies will harden as they cool.