Line a 9x13-inch pan with a thin smear of cream or parchment to help the first layer stick.
Beat cream cheese, powdered sugar, vanilla, and salt until smooth and fluffy.
Whip the cold heavy cream to stiff peaks in a chilled bowl.
Fold the whipped cream into the cream cheese mixture until no streaks remain.
Quickly dip cookies in cold milk and arrange a snug single layer in the pan.
Spread a generous layer of the cream mixture over the cookies. Spoon a thin layer of cherry pie filling over the cream.
Repeat layers—dipped cookies, cream, then cherries—until you reach the top, finishing with a smooth cream layer.
Swirl a few spoonfuls of cherry filling on top and sprinkle with chocolate shavings.
Cover tightly and refrigerate at least 4 hours, preferably overnight, until the cookies soften.
Slice cold and serve. Wipe the knife between cuts for clean layers.