In a medium bowl, whisk the flour with the baking soda, ginger, cinnamon, salt, allspice and white pepper. In a large bowl, using an electric mixer, beat the butter until creamy. Add the granulated sugar and the light brown sugar and beat at medium-high speed until light and fluffy, about 2 minutes. Beat in the egg and honey. Beat in the dry ingredients at low speed until combined. Transfer the dough to a sheet of plastic wrap, flatten into a disk and refrigerate until firm, about 30 minutes.
Preheat the oven to 350°. Line 3 baking sheets with parchment paper. Spread the turbinado sugar on a plate. Roll the dough into 1-inch balls and roll generously in the turbinado sugar. Transfer to the baking sheets, about 1 1/2 inches apart. Using a flat-bottomed glass, press each cookie to a 1 1/2-inch round. Working with one baking sheet at a time, bake the cookies for 15 to 16 minutes, until they are deeply golden and the tops are cracked. Cool the baking sheets on wire racks.
The cookies can be stored in an airtight container for up to 3 days.