Ashley’s Ice Cream in New Haven, CT (which does, by the way, easily rank in our top 5 ice cream places of all time) changes their menu regularly and always includes some sort of Oreo variation. The best is Coffee Oreo, but other favorites include Banana Oreo and Mint Oreo!
Also, although not Oreo-brand cookies per se, Ben and Jerry’s Vermonty Python ice cream is fantastic. It is a coffee liqueur ice cream with a chocolate cookie crumb swirl & fudge cows. Delicious.