In a medium bowl, beat cream cheese, sweetened condensed milk and cream with an electric mixer until smooth. Gradually mix in lime juice until mixture reaches the consistency of pudding.
Dip each cookie in the reserved peach juice, then place cookies side by side in a 9x13 inch pan, until the bottom of the pan is covered with cookies. Spread half of the cream cheese mixture over the cookies. Repeat the cookie and filling layers once.
Top the dessert with the drained peaches. Refrigerate for at least 2 hours, or until firm.
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Notes
I used Pepperidge Farm Chessmen cookies in this recipe. If you use a thinner shortbread, you may want to make three layers rather than two.