Using a stand mixer or hand held mixer with the whisk attachment, on medium high speed, whip the cold heavy whipping cream until you have firm peaks. (Firm peaks are when you pull the whisk out of the cream and a peak with a sharp tip forms and holds its shape). This will take 2-3 minutes.
Turn the mixer to low speed and sprinkle in the powdered sugar. Next slowly pour in the sweetened condensed milk, whisk until it is combined, about 20 seconds. Add the lime juice and lime zest. Whisk for an additional 20 seconds. Set aside.
Place the cookies in a large sealable plastic baggie. Crush the cookies- using a rolling pin, smooth meat mallet, or small frying pan works great. Do not crush it to dust, just to smaller bite sized pieces. Like the size of a nickel or dime.
With a spatula fold the cookies into the cream mixture.
Gently pour/scrape the mixture into a freezer safe glass or metal loaf pan. Cover and freeze for 6+ hours.