In a small bowl, whisk together the cornstarch, warm water, and lemon juice until smooth.
In a saucepan, cook raspberries with sugar over medium heat for about 3 minutes, stirring constantly. Add the cornstarch mixture and simmer for an additional 3 minutes, gently crushing the raspberries as they soften.
Once thickened, blend the raspberry mixture and strain it to remove seeds. Set aside to cool.
Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
In a small bowl, mix the graham cracker crumbs, melted butter, and sugar. Press the mixture into the bottom and sides of the prepared pan.
Bake the crust for 10 minutes and set it aside to cool. Wrap the pan’s exterior with aluminum foil to keep water out during the water bath.
Lower the oven temperature to 300°F (148°C). Using low speed, blend the cream cheese, sugar, and flour in a large bowl until smooth.
Stir in the sour cream, lemon juice, and zest until incorporated.
Add the eggs one by one, followed by the egg yolks, mixing slowly after each addition.
Gently mix a couple of tablespoons of cheesecake filling into the raspberry filling. Pour about three-quarters of the cheesecake mixture into the cooled crust.
Drop spoonfuls of the raspberry mixture onto the cheesecake and swirl them with a spatula. Add the remaining cheesecake filling and swirl with more raspberry filling on top.
Place the springform pan inside a larger pan. Add warm water until it reaches halfway up the springform pan, being careful not to let any water seep into the cheesecake.
Bake for 1 hour 25 minutes until the center is mostly set but still has a slight jiggle.
Turn off the oven and leave the cheesecake inside for 30 minutes. Afterward, crack open the oven door and let the cheesecake cool for another 30 minutes.
Transfer to the fridge to cool completely, then remove from the springform pan. Garnish with raspberries and lemon slices before serving.