At LEAST 24-48 Hours Before, Freeze Ice Cream Maker. If needed, make sure to freeze the bowl or insert for your ice cream maker in advance. Otherwise, the ice cream will not churn properly.
Make The Ice Cream Base. In a medium saucepan, combine heavy cream, whole milk, sugar, and salt. Whisk over medium-low heat just until the sugar is dissolved. (It's ok if the mixture doesn't get hot, the sugar just needs to be dissolved.) Remove from heat and stir in vanilla.
Chill. Transfer the vanilla ice cream base to a large liquid measuring cup or glass container and refrigerate at LEAST 2-3 hours, or until very cold all the way through. (Otherwise, it will not churn.)
Churn Ice Cream according to your ice cream maker's instructions. For me, that means placing the chilled insert into the ice cream maker, turning it on and pouring the cold ice cream mixture into the chilled insert. Cover and let it churn 20-30 minutes, or until the texture of rich soft-serve ice cream.
Mix In Oreos. During the last minute or two of churning the ice cream, gradually add the chopped gluten-free Oreo pieces and let the ice cream maker mix them in.
Freeze. Transfer the ice cream mixture into a freezer-safe container. Sprinkle with additional Oreo pieces, as desired, and freeze for at LEAST 4-6 hours, or until firm enough to scoop.
Serve & Store. Scoop and enjoy! Leftover cookies & cream ice cream will keep up to 1 week in the freezer, though it will continue to harden with time.