Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs with ½ cup of granulated sugar and melted unsalted butter until well blended. Press the mixture into the bottom of a 9-inch springform pan. Bake for 10 minutes and cool completely.

In a large mixing bowl, beat four packages of cream cheese with an electric mixer until smooth. Gradually add ¼ cup of granulated sugar and 1 teaspoon of vanilla extract, mixing well. Incorporate eggs, one at a time. Stir in lemon juice, zest, and 1 cup of sour cream.

In a saucepan, combine fresh raspberries, ¼ cup of sugar, juice from half a lemon, 1 tablespoon of cornstarch, and 1 tablespoon of water. Cook for 5–7 minutes until thickened. Remove from heat and cool slightly.

Pour the cheesecake filling into the prepared crust. Dollop spoonfuls of the raspberry sauce over the filling. Swirl the raspberry sauce into the filling to create marbled patterns.

Bake the cheesecake for 60–70 minutes until edges are set and center jiggles slightly. Turn off the oven and crack the door open, letting it cool inside for 1 hour.

Let the cheesecake cool at room temperature for 30 minutes, then cover and refrigerate for at least 4 hours, preferably overnight.