Dough: Beat together butter and sugars together until smooth, then add in the egg and vanilla. In a separate bowl, combine flour, cinnamon, nutmeg, cloves, ginger, pepper, salt, and baking soda. Fold the flour mixture into the butter mixture.
Bake: Preheat oven to 375°F (190°C). Roll dough into balls and flatten into big cookies. Place on a parchment paper lined baking sheet and bake for 15 to 20 minutes, or until cookies are browned around the edges and a bit crispy. Remove all but 2 cookies. Continue cooking these 2 cookies for 10 more minutes, until very crispy.
Blend: Meanwhile, cool the rest of the cookies to room temperature, then add them to a food processor and pulse until they are fine crumbs. With the food processor running, slowly pour in melted butter, then coffee, then milk (you may not need all the milk!) Continue blending and adding milk until the consistency is a smooth paste. Crush the 2 remaining cookies into crumbs and mix into the cookie butter for added crunch.