Preheat oven to 350°F. Line a large baking sheet with parchment paper or non-stick foil.
With an electric mixer or a wire whisk, beat butter and sugar until fluffy. Add egg and beat just until combined. Mix in baking soda and salt, making sure there are no lumps of baking soda. Stir in the buttermilk and vanilla, then add the flour and stir until it is well mixed.
Spoon quarter cups of batter about 3 inches apart onto baking sheet. Bake in middle of oven until tops are puffed and pale golden, and cookies spring back when touched, 15 to 17 minutes. Transfer to a cooling rack and cool to room temperature.
Icing: Stir together confectioners’ sugar, corn syrup, lemon juice, vanilla, and 2 tablespoons water. Transfer half of icing to another bowl and stir in cocoa, adding more water slowly until you get a nice spreading consistency.
Dye the remaining white icing orange, using yellow food coloring a tad of red.
Ice the cookies ½ orange and ½ white. Traditional black & whites are iced on the flat side rather than the rounded side, but I iced it on the rounded side.
Allow icing to set before serving cookies.
Makes about 8 cookies