Cream together butter and peanut butter. Add sugars, vanilla and egg. Mix until combined. In a separate bowl, mix flour, salt and baking soda. Add dry ingredients in small amounts to wet ingredients. Once this mixture is combined, pat into a 9 X 13 in pan and bake for about 20 minutes.
Sprinkle chocolate chips over mixture in pan while it's still warm. As they melt, spread the chocolate chips evenly onto cookie mixture with a rubber spatula.
Cool in refrigerator for 20 minutes. Meanwhile, beat together powdered sugar, remaining peanut butter and milk until the mixture reaches a smooth consistency. Spread the powdered sugar mixture over cooled cookie and chocolate bars in pan. Cut into bars.