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.
5 tablespoons unsalted butter, 3/4 cup granulated sugar, 1 large egg, 1 tablespoon red food coloring, 1 teaspoon pure vanilla extract, 1/2 cup buttermilk
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 powdered sugar, 1/2 teaspoon vanilla, 1 tablespoon corn syrup, and hot water until smooth.
2 cups powdered sugar, 1 tablespoon corn syrup, 1/2 teaspoon vanilla extract, 2 tablespoons hot water
In another bowl, combine the chocolate, butter and corn syrup; microwave until melted, about 1 minute.