Preheat the oven to 350°F. Line 2 (18 x 12-inch) baking sheets with parchment paper. In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In another large bowl, combine the sugar and butter and beat until creamy, about 5 minutes. Add the milk and vanilla and beat until incorporated. Add the flour mixture to the butter mixture in batches, beating after each addition, until combined.
Scoop the dough, 1/4 cup at a time, onto the prepared baking sheets, spacing the scoops 3 inches apart. Flatten them slightly with your hands (keep your hands wet to prevent the dough from sticking). Allow room between the scoops as the cookies will spread as they bake.
Bake the cookies for 15 minutes or until a toothpick inserted in the center comes out clean. Allow the cookies to cool 2 minutes on the baking sheets and then carefully flip the cookies over and transfer them, upside down, to a wire rack to cool completely.
While the cookies are cooling, make the icing. In a large mixing bowl, combine the confectioners’ sugar, boiling water, and vanilla. Mix well to get a spreadable icing. Add a little more water, if needed. Using an offset spatula, spread a thin layer of icing onto the flat side, the former bottom, of each cookie. Return the cookies to the wire rack to dry. You should have about 1/2 cup of icing left.
While the white icing is drying, melt the chocolate chips in a microwave or double boiler. When the chips are all melted and smooth, whisk the melted chocolate into the remaining icing. The chocolate icing should be thicker than the white, but still be spreadable. If it is too thick, add a little hot water to thin it out. Use the offset spatula to frost one half of each cookie over the white icing. Return the cookies to the wire racks to dry. Store leftovers in a covered container for up for 5 days.