Preheat the oven to 375 degrees F (190 degrees C).
Cream together 1 cup butter and egg. Add 1 cup white sugar, vanilla, and hot water. Stir in flour, cocoa, and baking soda and mix well.
Drop from a teaspoon onto cookie sheets and bake in the preheated oven for 10 to 12 minutes; set aside to cool.
To make peanut butter frosting: Blend 1 tablespoon butter and peanut butter together until smooth. Stir in confectioners' sugar and add enough milk to make frosting soft enough to spread. Spread between the flat sides of two cookies and sandwich together. Repeat with remaining cookies.