Preheat the oven to 350°. Line a baking sheet with parchment paper. In a medium bowl, sift together the flour, cocoa, baking soda and salt.
Using a mixer, beat 5 tablespoons butter with the granulated sugar until fluffy, 3 minutes. Beat in the egg, food coloring and 1 teaspoon vanilla. Beat in the flour mixture alternately with the buttermilk until smooth
Place 1/4-cup scoops of batter 2 inches apart on the prepared baking sheet; spread out. Bake until a toothpick inserted in the center comes out dry, 12 to 15 minutes. Let the cookies sit for 5 minutes, then transfer to a rack to cool.
In a bowl, whisk together the confectioners' sugar, remaining 1/2 teaspoon vanilla, 1 tablespoon corn syrup and 2 tablespoons hot water until smooth. In another bowl, combine the chocolate, remaining 3 tablespoons butter and 1 tablespoon corn syrup; microwave until melted, about 1 minute.
Coat the cookies with the vanilla, then the chocolate icing. Refrigerate until set, about 20 minutes.