Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with both sugars until fluffy. Add in the egg and vanilla extract and mix until smooth.
Add in the flour mixture, and mix until it is fully combined. Fold in the chocolate chips. Roll the cookie dough into balls, and place them onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes. Let cool completely.
For the filling, combine butter with powdered sugar, vanilla extract, and milk until smooth. Place the filling evenly onto half of the cooled cookies. Sandwich with another cookie.
