Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, cream together the butter, brown sugar, and granulated sugar until light and fluffy.
Add the eggs and vanilla extract, and beat until well combined.
In another bowl, whisk together the flour, baking soda, and salt. Gradually add this to the wet mixture, mixing until just combined.
Stir in the chocolate chips.
Drop spoonfuls of dough onto the prepared baking sheet. Bake for 10-12 minutes, or until the edges are golden brown. Let cool completely.
Once the cookies are cool, place a scoop of softened vanilla ice cream between two cookies. Press gently to spread the ice cream to the edges.
Wrap each sandwich in plastic wrap and freeze for at least 1 hour before serving.