Preheat your oven to 350°F (175°C).
In a mixing bowl, cream together the butter, brown sugar, and granulated sugar until light and fluffy.
Add the eggs and vanilla extract, and mix until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add to the wet ingredients, mixing until just combined.
Stir in the chocolate chips.
Drop spoonfuls of dough onto a baking sheet and bake for 10-12 minutes, or until golden brown. Let cool completely on a cooling rack.
For the filling, beat the butter until creamy. Gradually add the powdered sugar, milk, and vanilla extract, and beat until smooth.
Spread the filling on the flat side of one cookie and top with another cookie to make a sandwich. Repeat with remaining cookies.