In a large mixing bowl, whip the cold heavy cream until stiff peaks form. This will create the base texture of your ice cream.
In another bowl, whisk together the sweetened condensed milk, vanilla extract, and blue food coloring. Adjust the color to your liking. Fold this mixture gently into the whipped cream until fully combined.
Fold in the crumbled chocolate chip cookies, Oreo pieces, and any additional mix-ins like mini chips or cookie dough bits.
Pour the mixture into a loaf pan or freezer-safe container. Smooth the top with a spatula and add a few extra cookie pieces on top for a decorative touch. Cover and freeze for at least 5–6 hours or overnight until firm.