Preheat the oven to 350°F.
In a mixing bowl, whisk together the 2 ½ cups all-purpose flour, 1 tsp baking powder, and 1 tsp salt.
In the bowl of an electric mixer, cream together the ½ cup unsalted butter and 1 cup granulated sugar until light and fluffy, for about 3 minutes on medium speed.
Beat in the 2 large eggs one at a time, then add the ½ cup whole milk and 1 tsp vanilla extract.
Gradually mix in the dry ingredients until a smooth dough forms.
Drop 12 spoonfuls of dough onto the prepared baking sheet, spacing them about 2 inches apart (depending on the size of your baking sheet you may need two separate sheets).
Bake for 15 minutes or until the edges are lightly golden brown.
Let the cookies cool completely on the baking sheet.
While the cookies are cooling, make the icing by mixing together the 3 cups powdered sugar, ¼ cup light corn syrup, ¼ cup whole milk, and ½ tsp vanilla extract until smooth.
Transfer half of the icing to a separate bowl and stir in melted 2 ounces semisweet chocolate.
Once the cookies are cool, flip them over so that the flat side is facing up. Spread the white icing onto one half of each cookie using a knife or an offset spatula. Let the white icing set for about 15 minutes, then spread the chocolate icing onto the other half of each cookie.
Let the cookies sit for about an hour or until the icing is firm.