Place the Oreo cookies in a large zip-top bag and seal tightly. Crush the cookies into large pieces with a wooden spoon or rolling pin. Do not finely crush them.
In a large bowl, stir together the sweetened condensed milk and vanilla extract.
In a separate bowl, beat the cold heavy whipping cream with a stand mixer or hand mixer for 2–3 minutes, until stiff peaks form.
Gently fold the whipped cream into the sweetened condensed milk mixture until just combined. Fold in the crushed Oreo cookies, being careful not to overmix.
Spread the mixture evenly into a 9-inch loaf pan. Cover with foil and freeze for at least 6 hours, or until firm.