Preheat an oven to 350 degrees F (175 degrees C). Whisk together the all-purpose flour, buckwheat flour, cornstarch, white sugar, baking soda, salt, cinnamon, ginger, allspice, dry mustard, and ground black pepper in a large mixing bowl.
Stir together the molasses, oil, vinegar, vanilla, and cold water in a measuring cup. Make a well in the center of the dry ingredients; pour the wet ingredients into the well. Mix the batter together until just blended. Pour the batter into an ungreased 8x8 inch baking pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.