Creating this Velvety Raspberry Swirl Cheesecake is a rewarding process. Follow these step-by-step instructions to bake your way to dessert heaven:

Step 1: Prepare the Graham Cracker Crust

1. Preheat your oven to 350°F (175°C). This ensures the crust bakes evenly and sets properly.
2. In a medium bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Mix thoroughly until all the crumbs are evenly moistened and the mixture resembles wet sand.
3. Press the crumb mixture firmly into the bottom of a 9-inch springform pan. Use the bottom of a measuring cup or a flat-bottomed glass to evenly press the crumbs into a compact layer. You can also bring the crust slightly up the sides of the pan if desired.
4. Bake the crust for 8-10 minutes. This pre-baking helps to set the crust and prevent it from becoming soggy.
5. Remove the crust from the oven and let it cool completely while you prepare the cheesecake filling.

Step 2: Make the Velvety Cheesecake Filling

1. Reduce the oven temperature to 325°F (160°C). Lowering the temperature helps to bake the cheesecake gently and prevent cracking.
2. In a large bowl, beat the softened cream cheese and granulated sugar together until smooth and creamy. Use an electric mixer (stand mixer or hand mixer) for best results. Scrape down the sides of the bowl as needed to ensure everything is evenly incorporated.
3. Beat in the eggs one at a time, mixing well after each addition. Be careful not to overmix at this stage, as this can incorporate too much air into the batter and lead to cracks in the cheesecake.
4. Stir in the sour cream and vanilla extract until just combined. Mix until the batter is smooth and homogenous. Again, avoid overmixing.

Step 3: Create the Raspberry Swirl

1. In a small saucepan, combine the fresh raspberries, granulated sugar, and lemon juice.
2. Cook over medium heat, stirring occasionally, until the raspberries have softened and released their juices. This usually takes about 5-7 minutes.
3. Reduce the heat to low and simmer for another 5-7 minutes, or until the raspberry mixture has thickened slightly. The mixture should be syrupy but still slightly fluid.
4. Remove the saucepan from the heat and let the raspberry mixture cool slightly.
5. Pour the raspberry mixture into a blender or food processor and puree until smooth. If you prefer a seedless raspberry swirl, you can strain the puree through a fine-mesh sieve to remove the seeds.

Step 4: Assemble and Bake the Raspberry Swirl Cheesecake

1. Pour the cheesecake filling over the cooled graham cracker crust in the springform pan. Spread the filling evenly.
2. Spoon dollops of the raspberry puree over the cheesecake filling. Use a spoon or a small piping bag to create decorative dollops.
3. Use a knife or a toothpick to gently swirl the raspberry puree into the cheesecake filling. Create a marbled or swirled effect by dragging the knife or toothpick through the dollops of puree. Be careful not to over-swirl, as this can muddy the colors.
4. Bake in the preheated oven for 60-70 minutes, or until the cheesecake is set around the edges and slightly jiggly in the center. The center should still have a slight wobble, as it will continue to set as it cools.
5. Turn off the oven and leave the cheesecake in the oven with the door slightly ajar for 30 minutes. This gradual cooling process helps to prevent cracking.
6. Remove the cheesecake from the oven and let it cool completely at room temperature.
7. Cover the cheesecake tightly with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow it to fully chill and set. Chilling is crucial for achieving the perfect texture and flavor.

Step 5: Unmold and Serve

1. Once the cheesecake is thoroughly chilled, gently run a thin knife or spatula around the edge of the springform pan to loosen the cheesecake.
2. Release the springform pan and carefully remove the sides.
3. Transfer the Velvety Raspberry Swirl Cheesecake to a serving plate or cake stand.
4. Serve chilled and enjoy!