Preheat oven to 350°F. Line large baking sheets with parchment paper or silicone baking mats. Set aside.
In a large bowl using a hand-held mixer or stand mixer with the paddle attachment, beat the butter on medium speed until completely smooth and creamy. Add the sugar and light brown sugar and mix on medium speed until fluffy and light in color. Mix in eggs one at a time and scrape down the sides and bottom of the bowl after each addition. Mix in vanilla.
In a separate bowl, sift together flours, baking soda and salt. On low speed, slowly add flour mixture into butter mixture until combined.
Add the chocolate chips and mix by hand just until evenly distributed.
Scoop dough, about 3 tablespoons each, and place on prepared baking sheets leaving 2 inches between each cookie. Bake 16-18 minutes, until edges are golden brown. Remove from oven and allow to cool for 2 minutes on the cookie sheet. Transfer to a cooling rack and cool completely.
Place a scoop of ice cream on a cookie and top with a second cookie. Gently push down and repeat with the rest of the cookies. Freeze sandwiches at least 1 hour before serving.