Stir butter, sugar, and honey together in a large saucepan over low heat until butter is melted and sugar is dissolved. Cool for 10 minutes.
Mix all-purpose flour, cake flour, whole wheat flour, cinnamon, baking soda, cloves, nutmeg, and ginger together in a bowl.
Beat flour mixture and eggs into cooled butter mixture until a smooth, soft dough forms. Cover the saucepan with aluminum foil and set in a cool place to ferment, 1 to 3 days.
Preheat oven to 375 degrees F (190 degrees C). Line baking sheets with parchment paper or silicone baking mats.
Divide dough into long ropes about 2/3-inch in diameter. Cut ropes into 1 1/2-inch sections. Roll each piece of dough into a walnut-size ball. Place balls 1 1/2 inches apart on prepared baking sheets. Press a walnut piece halfway into the top of each cookie.
Bake cookies in the preheated oven until slightly golden, 10 to 12 minutes.