For the berry jam, combine all ingredients for the jam in a medium-sized saucepan over medium heat, and stir together.
Stir berries until the mixture begins to boil and berries start to burst, then reduce heat to low and cover. Cook for 5-10 minutes, stirring occasionally, until mixture has thickened to a jam-like consistency. Set aside to cool.
For the graham cracker crust, place the two boxes-worth of graham crackers into a food processor and pulverize until you have a fine powder (no chunks). Adding 4 tablespoons-worth of softened butter pieces at a time, pulse the food processor with the butter. Continue for the rest of the butter, until the graham cracker crust comes together in a flaky, slightly-crumbly dough.
Pat the graham cracker crust into the bottom of a 9x13 inch pan and slightly up the sides to create a 1/4 inch thick crust.
For the cheesecake filling, add the condensed milk, cream cheese, lemon juice, and vanilla extract to a large bowl, then beat with an electric mixer or stand mixer for 2-3 minutes, until mixture is smooth and fluffy.
Pour the cheesecake filling on top of the crust, smoothing to even it out, then swirl in the berry jam.
Refrigerate for 4 hours, then slice and serve!