Preheat the oven to 350°F (177°C). Line two light-colored aluminum 13-by-18-inch half-sheet pans with parchment. Whisk together the flour, baking powder, cornstarch, salt, cinnamon, cardamom, ginger, allspice, and cloves.
Beat the butter and granulated sugar for about 3 minutes, until light and fluffy. Beat in the whole egg, egg yolk, and honey. Gradually mix in the dry ingredients on low just until combined. Scoop 1 1/2-Tbsp portions 2 inches apart and flatten gently with a spatula.
Bake for 12–14 minutes, until the cookies are just set and slightly golden while their centers remain soft. Cool on the pans for 2 minutes, then transfer to wire racks and cool completely.
Whisk the sifted powdered sugar with the espresso or strong coffee until thick but pourable. Drizzle over the cooled cookies and let the glaze dry completely before stacking or storing.