The Cookies: Set 2 racks in the middle of the oven and preheat to 350 degrees. In a medium bowl, stir together the flour, baking powder and salt. In the bowl of an electric mixer, beat the butter and sugar together for 15 seconds until smooth. Add the eggs, 1 at a time, beating until each is incorporated. Add the vanilla and lemon extracts and continue beating until fluffy, about 2 minutes. With the mixer on its slowest setting, gradually beat in 1/2 of the flour mixture. Beat in the milk and then the remaining flour mixture. On nonstick or parchment lined cookie sheets, drop 1/2 cup mounds of dough at 4-inch intervals. Bake the cookies for about 11 minutes, turning once for even baking, until the cookies are lightly tanned. Set the cookie sheets on a rack to cool. The Frosting: Fit a heavy-bottomed saucepan with a candy thermometer. Over high heat, cook the water, corn syrup, sugar and cream of tartar until it registers 240 degrees (soft ball). Off heat, vigorously whisk in the confectioners' sugar, vanilla and hot water until creamy looking. Quickly spread half of the icing on 1/2 of each cookie. Whisk the cocoa and hot coffee into the remaining icing. Spread it on the other halves of the cookies. Let set for 15 minutes.