Crush graham crackers into fine crumbs. Mix with granulated sugar and melted butter to form a crumbly paste. Press evenly into the bottom of a springform pan.
In a large bowl, combine cream cheese, sweetened condensed milk, lemon juice, and vanilla extract. Mix until smooth and well blended. Fold in chopped strawberries.
Pour the cheesecake mixture over the prepared crust. Smooth the top with a spatula. Cover and chill for 4 hours or until firm.
In a separate bowl, mix remaining strawberries, strawberry jam, and a pinch of sugar. Spread this mixture evenly over the chilled cheesecake. Optional: Add crushed cookies or cereal for crunch and sprinkle with red food coloring.
Chill for another hour before slicing. Serve chilled.