Place an 8-inch square pan and a large glass bowl in the freezer for 30 minutes.
Combine the jam and strawberries in a small saucepan over medium heat. Cook, stirring frequently, until the berries soften and the jam becomes liquidy, about 5 minutes. Set aside to cool.
Beat the cream cheese, sweetened condensed milk, vanilla and salt in a large bowl with a hand-held mixer until smooth. Set aside.
Wash and completely dry the beaters.
Beat the heavy cream in the large, chilled bowl with a hand-held mixer until stiff peaks form.
Fold the cream cheese mixture into the whipped cream.
Spoon half of the mixture into the frozen pan.
Reserve some of the cookies to sprinkle on top.
Sprinkle the cream mixture with half of the remaining crushed cookies and fold gently to incorporate the cookies in the cream.
Spoon half of the jam on top and swirl with a wooden skewer or chopstick.
Repeat the process with the remaining cream, jam and cookies.
Sprinkle the reserved cookies on top.
Cover tightly with plastic wrap and freeze until firm, at least 6 hours but preferably overnight.
To serve, let the ice cream stand at room temperature for about 5 minutes before scooping into serving bowls.