Place raspberries, sugar and water in a saucepan. Heat over medium heat until berries are soft and broken down.
1 ½ cups raspberries, 2 tablespoons sugar, 1 tablespoon water
Place berries through a sieve to remove all seeds
Refrigerate sauce until needed
Crust
Place graham crackers broken into chunks in a food processor along with melted butter and sugar.
9 graham crackers, ¼ cup butter, 2 tablespoons sugar
Process until coarse crumbs
Cover an 8 x 8 inch baking dish with 2 pieces of parchment paper (or a single piece of foil.) The parchment paper should be the same width as the pan and place so the paper crosses each other in the center with the paper overlapping on the sides. This will be used to remove the entire cheesecake from the pan after it is cooked and cooled.
Place crumbs on top of parchment paper and press down firmly using hands or the bottom of a flat measuring cup
Bake in a preheated 350° oven for 10 minutes
Filling
Place room temperature cream cheese in a bowl and mix with a mixer until smooth
16 ounces cream cheese
Add sugar, eggs, lemon juice, vanilla and salt. Mix together until smooth and creamy
½ cup sugar, 2 eggs, 1 tablespoon lemon juice, 1 teaspoon vanilla, ⅛ teaspoon salt
Place mixture over prepared crust and spread evenly over crust
Add dollops of the raspberry sauce over the filling. Use a butter knife to create swirls of the sauce and the filling. You might not need all the sauce.
Bake in preheated 350° oven for 30-35 minutes. Filling is done when there is just a slight jiggle in the center of the pan when you give a slight shake.
Allow cheesecake to cool at room temperature for 30-45 minutes and then place in the refrigerator to fully chill for at least 3 hours. Do not cover the cheesecake unless you are chilling for longer than 3 hours.
Remove cheesecake from pan by carefully pulling up on all 4 ends of the parchment paper. Place on a cutting board and slice into 2 inch squares. Garnish with fresh raspberries, if desired.
Notes
Make certain cream cheese is at room temperature before beginning otherwise your cream cheese will be lumpy
Do not overmix once you've added the additional ingredients. Just mix until smooth and creamy.
Make gentle swirls with the sauce and filling
Cheesecake is done when there is just a slight amount of jiggle in the center of the pan
Allow cheesecake to fully cool before removing from pan and slicing