In a medium bowl, whisk together flours, cinnamon, baking soda, baking powder, and salt. Using an electric mixer, cream butter, brown sugar, and honey until fluffy, 2 to 3 minutes. Scrape down sides of bowl. With mixer on low speed, add egg, and mix until combined, Add flour mixture, and mix until combined.
Turn out dough onto a lightly floured surface. Roll between two sheets of parchment to a 1/8-to-1/4-inch thickness. Remove top piece of parchment paper and place dough on a baking sheet. Refrigerate until firm, about 30 minutes.
Using a fluted pastry wheel, cut dough into 2 1/4-inch squares and prick dough with a fork to create dotted lines. Transfer to two parchment-lined baking sheets and freeze until firm, about 30 minutes.
Preheat oven to 350 degrees with racks in upper and lower thirds. Bake graham crackers until golden brown, rotating sheets from top to bottom and front to back halfway through, 12 to 14 minutes. Transfer crackers to a wire rack to cool completely.
Graham crackers can be stored in an airtight container at room temperature up to 1 week.