1. In the mixer's bowl, beat the cream until lightly whipped, then add the cream cheese and sweetened milk until the mixture is homogenized.
2.  Break the cookies into small pieces and put them in the mixture along with the peanut butter, vanilla and lime zest.
3. Place the ice cream mixture in a pan and place in the freezer for one day, stirring every 2-3 hours so that it does not make pellets.
4.  Serve with the caramel syrup.