Place the cream cheese in the body of a stand mixer with the paddle attachment. Mix until smooth with no lumps. Add in the pudding mix and mix to combine.
Add 1 cup of the cream and mix on slow speed until combined. Add 1 more cup of heavy cream, mix on slow to combine. Add in the key lime juice, mix on slow speed until combined and smooth, scrape down the sides as needed. Reserve ⅔ cup of this mixture.
Pour the remaining cream cheese mixture on top of the cookie crust and smooth it out with a spatula. Evenly spread the remaining cookie crumbs on top.
In the body of a stand mixer add the remaining 3 & ½ cups of the heavy cream and the powdered sugar. Using the whisk attachment, whip the cream and sugar starting on low speed and gradually increasing in speed to medium to form medium peaks. Take out about ⅓ of the whipped cream and set aside.
Fold the remaining whipped cream into the remaining ⅔ cup of the cream cheese mixture along with the lime zest. Pour this on top of the cookie crumbs in the baking dish, smooth out the top.
Top the whole thing with the remaining whipped cream. You can smooth it over the top or pipe a decoration on top like seen in the photos. Let it set in the fridge for at least 6 hours, or up to overnight.