Preheat the oven to 350 degrees F (175 degrees C).
Cream together the softened butter, brown sugar, and white sugar until smooth.
Beat in the eggs one at a time, then stir in the vanilla extract.
Combine the flour, baking soda, baking powder, and salt; gradually stir into the creamed mixture.
Fold in the chocolate chips.
Drop by large spoonfuls onto ungreased baking sheets.
Bake for about 10 minutes in the preheated oven, or until edges are nicely browned.
Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Pair cookies of similar sizes and place a scoop of softened vanilla ice cream with chocolate chips on the flat side of one cookie.
Gently press another cookie flat side down onto the ice cream to make a sandwich.
Wrap each ice cream sandwich individually with plastic wrap and place in the freezer until firm, about 1 hour.