Prepare the Base: In a medium mixing bowl, whisk together the heavy cream, whole milk, sugar, and vanilla extract until the sugar is fully dissolved.
Add the Blue Dye: Gradually add blue food dye to the vanilla base, starting with 5-6 drops if using liquid dye. Whisk well and adjust until you achieve the desired bright Cookie Monster blue color.
Prepare the Mix-Ins: Place Oreos and Chips Ahoy cookies in separate resealable plastic bags. Crush them into small pieces using a rolling pin or similar tool. Set aside.
Churn the Ice Cream: Assemble your Cuisinart ice cream maker according to the manufacturer’s instructions. Turn the machine on and pour the chilled blue vanilla base into the bowl. Let it churn for about 15-20 minutes, or until it starts to thicken.
Add Mix-Ins: Gradually add the crushed Oreos and Chips Ahoy to the ice cream maker during the last 5 minutes of churning
Freeze the Ice Cream: Once churned, transfer the soft ice cream into an airtight container. Press a piece of wax or parchment paper on top of the ice cream to prevent ice crystals from forming. Freeze for at least 2 hours.
Serve: Scoop into bowls or cones and enjoy your vibrant, cookie-filled Cookie Monster ice cream!