Preheat oven to 350 degrees F. Line two large baking sheets with parchment paper or silpat liners and set aside.
In the bowl of your stand mixer, cream together the butter and sugars until light and fluffy
Add egg, continue to beat for 1 minute
Beat in oil, milk, vanilla paste and root beer concentrate
Whisk together flour, cocoa powder, baking soda and salt in a large bowl
Add to butter mixture and mix until well combined. You may have to stop and scrape down the bowl of your mixer a few times.
Gently fold in white chocolate chips.
Use a large ice cream scoop or a #24 disher to create 6 big cookies per prepared baking tray.
Bake cookies for 18 minutes or until crisp on the edges. Let cool for 5 minutes on the cookie sheet and then move them to a cooling rack.
When the last batch of cookies is completely cool, remove ice cream from the freezer and allow to soften on the counter for about 10 - 15 minutes.
To assemble ice cream sandwiches, place 1/3 cup ice cream on bottom of a cookie. Top with a second cookie, pressing gently to flatten ice cream.
Repeat with remaining cookies and ice cream.
Place all the sandwiches on a baking sheet; freeze until firm, at least 2 - 3 hours.
Ice Cream Sandwiches are best eaten the day they are made!