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 mix until combined.
In another bowl, whisk together the flour, baking soda, and salt. Gradually add this to the wet ingredients, mixing until just combined.
Fold in the chocolate chips.
Drop spoonfuls of dough onto the prepared baking sheet, and bake for 10-12 minutes, or until the edges are golden brown. Let cool completely.
Once the cookies are cool, scoop a generous amount of softened ice cream onto the flat side of one cookie. Top with another cookie to make a sandwich. Repeat with remaining cookies and ice cream.
Wrap each sandwich in plastic wrap and freeze for at least 1 hour before serving.