Step 1

Whisk together the flours, spices, and salt. In a separate bowl, beat together the butter, sugars, honey, and vanilla with an electric mixer at medium-high speed until creamy, about 1 minute. Reduce the speed to low and mix in the flour mixture until just combined. The dough will be sticky.

Step 2

Roll out the dough between 2 sheets of parchment paper into a 10-inch square (about 1/4 inch thick) or place the dough in a large resealable plastic bag (not one with a pleated bottom) and smooth the dough with a rolling pin, filling the bag with the dough.

Step 3

Place the dough (still on the parchment or in the bag) on a baking sheet and refrigerate for 8 to 12 hours to allow the flavors to develop.

Step 4

Preheat the oven to 350°F (176° C), adjust the oven rack to the middle position.

Step 5

Remove the top layer of parchment or remove the dough from the bag. Trim the ragged edges of the dough. Cut twenty 1/2-inch-wide strips with a pastry wheel and a ruler. Cut each strip crosswise into fourths for a total of 80 cookies. If the dough begins to soften, refrigerate or freeze it until firm.

Step 6

Transfer about 30 cookies to an ungreased baking sheet with a spatula, arranging them 1 inch apart. Keep the unbaked cookies in the refrigerator or freezer. If the cookies on the sheet are no longer cold, chill or freeze until firm. Bake until the edges are several shades darker, 13 to 15 minutes. Cool the cookies on the baking sheet for 1 minute, then transfer to a wire rack to cool completely. Repeat with the remaining cookies.

Step 7

Whisk together all of the glaze ingredients until smooth.

Step 8

Tip the bowl of glaze on its side so the glaze is as deep as possible. Place a folded kitchen towel under the bowl for support. Dip half of a cookie into the glaze on a diagonal, letting any excess glaze drip off into the bowl and then scraping the bottom of the cookie on the edge of the bowl to remove any last extra drops of glaze. Set the cookie on a rack set over a baking sheet and immediately place a piece of candied orange peel on the glazed half of the cookie. Repeat with the remaining cookies, glaze, and candied orange peel.

Step 9

Let the cookies stand until completely set, about 1 hour. The cookies keep, layered between sheets of parchment paper in metal tins, at room temperature for up to 3 days.