Preheat oven to 375 degrees. Grease two large cookie sheets, or line with parchment paper.
Whisk together the flour, cocoa powder, baking soda and salt.
In the bowl of a standing mixer, cream the butter and sugars together, 2-3 minutes. Add the egg and continue beating until fluffy, 1-2 minutes longer. Beat in milk and vanilla extract. Finally, beat in flour mixture to combine.
Drop by heaping tablespoons onto prepared cookie sheets (you should get 12-14 cookies).
Bake for 10-14 minutes, until top springs back when touched.
Cool completely. Spoon a heaping tablespoon of frosting on the flat half of one cookie, then top with another cookie. Repeat.
Put 1/4 cup of sugar and water in saucepan over medium-high heat. Do not stir of you will get sugar crystals, but you can swirl the saucepan gently. It will bubble itself into a deep amber. Remove immediately from heat and add cream (careful - it will bubble up furiously). Stir until smooth and set aside.
Put the egg whites, salt, and 1/4 cup sugar in a heatproof bowl over a pot of simmering water. Whisk until sugar dissolves and mixture reaches 140 degrees. Transfer to bowl of standing mixer.
Beat on high until stiff peaks form. Add butter a bit at a time, and continue beating on medium. Reduce speed to low, add vanilla extract, and then caramel (you may need to gently rewarm the caramel in the microwave for 10 seconds at a time until it is workable but not burning hot). Beat for 4-5 minutes.