Make the cookie dough: Add the brown sugar, melted butter, and vanilla to a medium bowl and stir to combine evenly. Add ½ cup of flour, stir for 20–30 seconds, then add the remaining ½ cup of flour and mix until fully combined and a soft and smooth dough forms. Add the mini chocolate chips and mix until evenly incorporated Cover and chill in the refrigerator for 10 minutes.
Make the ice cream base: In a blender or food processor, combine cottage cheese, pudding mix, and milk and blend for 20 seconds, or until smooth.
Roll half of the cookie dough into roughly ½-inch-wide balls. Reserve the rest for another use; it will keep in an airtight container in the refrigerator for up to 3 days.
Add alternating layers of the cottage cheese mixture and cookie dough balls to a freezer-safe container, such as a plastic pint container or loaf pan.
Cover and freeze the ice cream for 4–5 hours, stirring every hour, until frozen.
Remove from the freezer and scoop into serving bowls.