Make one batch of edible cookie dough and roll the cookie dough into tiny balls or separate into little chunks. Set aside.
In a medium bowl, stir together the sweetened condensed milk and vanilla. Set aside.
In the bowl of a stand mixer or a large bowl with a hand mixer, beat cream on high until stiff peaks form, about 4 minutes. With a rubber spatula, gently fold condensed milk mixture into whipped cream. Stir in chocolate chip cookie dough chunks.
Pour ice cream mixture into a 9x9 loaf pan. Cover with plastic wrap or foil and place in the freezer until firm, about 6 hours.
Scoop into bowls and enjoy!