Arrange a rack in the middle of the oven and preheat it to 325° F (165° C).
Combine raspberries, sugar, and lemon juice in a small saucepan. Mash them and reduce the liquid over medium heat for about five minutes.
Prepare a slurry by mixing cornstarch with a tablespoon of water. Stir it in.
Let it thicken for about a minute to get a consistency like jam. Let it cool.
Pulse graham crackers into fine crumbs in a food processor or smash them in a zip-top bag.
Add melted butter, brown sugar, and salt and process until incorporated.
Spread the graham cracker mixture into the pan. Pack them down with a ramekin or the bottom of a glass.
Bake it for 10 minutes, then let it cool.
Combine cream cheese, sour cream, sugar, flour, salt, vanilla, lemon juice, and lemon zest in a large bowl. Beat on medium-low speed until smooth. Scrape the bottom and sides as needed with a rubber spatula.
Add eggs and mix until just combined. Overmixing can cause cracks on the surface.
Pour the mixture over the cooled crust and spread it evenly with a spoon.
Drop spoonfuls of the raspberry sauce on top.
Create swirls using a knife, chopstick, or skewer.
Bake for 30 minutes until set. The cheesecake is done when the center is set and no longer wet.
Let it cool completely in the pan uncovered. Refrigerate at least four hours before serving.