Place the chilled whipping cream into the bowl of a stand mixer fitted with a whisk attachment.
Whip the cream on medium speed until stiff peaks form.
In a large bowl, combine the sweetened condensed milk and vanilla. Whisk to combine.
Scoop half the whipped cream into the milk mixture. Carefully fold the whipped cream into the milk mixture, taking care not to deflate the cream.
Fold in the remaining whipped cream to the milk mixture, folding until thoroughly mixed.
Chop up the shortbread into bite sized pieces.
Layer the ice cream in a 9x5 loaf pan or pan of your choice, in three layers, alternatively with the shortbread, and swirl to mix just a bit.
Cover loosely with plastic wrap and freeze until solid, or overnight before serving.