1. Prepare the Crust:

• Preheat Oven: Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan. Line the bottom with a circle of parchment paper for easy removal.
• Combine Ingredients: In a medium bowl, combine the graham cracker crumbs and granulated sugar. Pour in the melted butter and stir until the crumbs are evenly moistened.
• Press into Pan: Press the crumb mixture firmly into the bottom of the prepared springform pan. Use the bottom of a measuring cup or a flat-bottomed glass to create an even layer.
• Bake Crust: Bake the crust for 8-10 minutes, or until lightly golden and set.
• Cool Crust: Remove the crust from the oven and allow it to cool completely on a wire rack while you prepare the raspberry swirl and filling. Keep the oven preheated.

2. Prepare the Raspberry Swirl:

• Cook Raspberries: In a small saucepan, combine the raspberries (fresh or frozen), sugar, and cornstarch.
• Thicken: Cook over medium heat, stirring frequently and mashing the raspberries slightly with the back of a spoon, until the raspberries break down and the mixture thickens, about 5-7 minutes.
• Strain Sauce: For a smooth swirl, strain the raspberry mixture through a fine-mesh sieve into a small bowl, pressing gently on the solids to extract the sauce. Discard the seeds/solids.
• Cool Sauce: Set the raspberry sauce aside to cool slightly while you prepare the cheesecake filling.

3. Prepare the Cheesecake Filling:

• Beat Cream Cheese: In a large mixing bowl, using an electric mixer (stand mixer with paddle attachment or hand mixer), beat the softened cream cheese on medium speed until completely smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
• Add Sugar: Gradually add the 1 cup of granulated sugar and continue beating until well combined and smooth.
• Add Eggs: Add the room-temperature eggs one at a time, mixing on low speed until just combined after each addition. Do not overmix.
• Incorporate Flavorings: Add the room-temperature sour cream, vanilla extract, fresh lemon juice, and lemon zest to the cream cheese mixture. Beat on low speed until everything is fully incorporated and the mixture is smooth.

4. Assemble the Cheesecake:

• Layer Filling: Pour half of the cheesecake filling over the cooled crust, spreading it evenly with a spatula.
• Add Raspberry Swirl: Drop small spoonfuls (about 1/2 teaspoon each) of the cooled raspberry sauce randomly over the first layer of filling.
• Add Remaining Filling: Gently pour the remaining cheesecake filling over the top.
• Add More Swirl: Drop more small spoonfuls of the raspberry sauce over the top layer of filling.
• Swirl: Use a toothpick, skewer, or the tip of a knife to gently swirl the raspberry sauce through the cheesecake filling, creating a marbled effect. Do not overmix the swirl.

5. Bake the Cheesecake:

• Water Bath (Optional but Recommended): Wrap the outside of the springform pan tightly with several layers of heavy-duty aluminum foil. Place the wrapped pan in a larger roasting pan. Carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan. This helps the cheesecake bake evenly and prevents cracks.
• Bake: Carefully transfer the roasting pan (or just the springform pan on a baking sheet if not using a water bath) to the preheated oven. Bake at 325°F (163°C) for 55-65 minutes, or until the edges of the cheesecake are set and the center is still slightly jiggly when the pan is gently shaken.

6. Cool and Chill:

• Cool in Oven: Turn off the oven. Let the cheesecake cool in the oven with the door cracked open slightly for 1 hour.
• Cool at Room Temperature: Remove the cheesecake from the oven (and water bath, if used). Carefully remove the foil wrap. Let the cheesecake cool completely at room temperature on a wire rack.
• Chill: Once cooled to room temperature, cover the cheesecake loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, until completely chilled and set.

7. Serve: Carefully remove the sides of the springform pan before serving. Slice the cheesecake with a sharp, clean knife (wiping the blade clean between cuts helps). Garnish with fresh raspberries and a dusting of powdered sugar, if desired.