In a large bowl combine the condensed milk and the vanilla extract.
In another large bowl, whip the heavy cream in a large bowl until medium stiff peaks are formed, a couple minutes on high.
Fold the whipped cream into the sweetened condensed milk.
Pour about 1/4 of the ice cream mixture into your 9x5 inch pan.
Sprinkle some of the cookie dough pieces on top of your ice cream mixture. Swirl the cookie dough pieces through, so they are spread throughout the ice cream. Add a few more pieces on top if needed.
Sprinkle with about 1-2 TBS of your mini chocolate chips, and swirl those throughout too.
Repeat with another 1/4 of ice cream, 1/4 of cookie dough and 1-2 TBS chocolate chips.
Repeat with the final layer, topping it with cookie dough pieces (roll them into balls to look nice if desired), and a few chocolate chips.
Cover with plastic wrap or foil and place in freezer for 6 hours, or overnight. Scoop and enjoy.