Prepare the cookie dough pieces first. Cream the softened butter with both sugars until smooth. Add milk and vanilla extract, mixing until combined.
Slowly add flour and a pinch of salt, mixing until the dough forms. Stir in mini chocolate chips. Chill the dough in the refrigerator.
Melt the butter for the ice cream in a saucepan over medium-low heat until browned. Transfer to a bowl and stir in brown sugar. Let cool.
Whisk in sweetened condensed milk and vanilla extract until well combined.
In a separate bowl, whip the cold heavy cream until stiff peaks form. Fold half of the condensed milk mixture into the whipped cream, then fold in the rest.
Add most of the mini chocolate chips, folding them in evenly. Save some for topping.
In a freezer-safe container, spread half of the ice cream base. Pinch off small pieces of cookie dough and sprinkle them over the ice cream. Add the remaining ice cream on top.
Finish by scattering the remaining cookie dough pieces and chocolate chips on top. Cover and freeze for at least 12 hours.
Scoop and enjoy your homemade cookie dough ice cream!
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Notes
Store in an airtight container in the freezer for up to 2 weeks. Press plastic wrap directly onto the surface before sealing.