Preheat your oven to 350°F (175°C). Wrap the outside of a 9-inch springform pan tightly with heavy-duty aluminum foil, covering the bottom and sides completely to prevent water from entering during the water bath.

In a medium bowl, combine the graham cracker crumbs and 1/4 cup granulated sugar. Pour in the melted butter and mix until all crumbs are moistened.

Press the crumb mixture firmly and evenly into the bottom of the prepared springform pan. You can use the bottom of a flat glass or measuring cup to help compact it.

Bake the crust for 8-10 minutes, or until lightly golden. Remove from the oven and set aside to cool slightly while you prepare the filling. Reduce oven temperature to 325°F (160°C).

In a small saucepan, combine raspberries, 1/4 cup granulated sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the raspberries break down and the mixture starts to simmer, about 5-7 minutes.

In a small bowl, whisk together cornstarch and water to create a slurry. Add the slurry to the simmering raspberry mixture, stirring constantly. Continue to cook for another 1-2 minutes until the sauce thickens.

Remove from heat. For a smoother sauce, press the mixture through a fine-mesh sieve to remove seeds. Let the raspberry swirl cool completely.

In a very large mixing bowl, using an electric mixer on medium speed, beat the softened cream cheese until completely smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl.

Gradually add 1 1/2 cups granulated sugar to the cream cheese, beating until just combined and smooth. Do not overmix.

Add the sour cream and heavy cream, mixing on low speed until just incorporated. Scrape down the sides of the bowl again.

Beat in the vanilla extract, lemon zest, and all-purpose flour until just combined.

Add the eggs one at a time, beating on low speed after each addition until just incorporated. Add the egg yolk last, mixing until just combined. Be careful not to overmix the batter once the eggs are added, as this can introduce too much air and cause cracks.

Pour about two-thirds of the cheesecake batter over the cooled crust in the springform pan.

Drizzle about half of the cooled raspberry swirl over the batter. Use a butter knife or a skewer to gently swirl the raspberry sauce into the batter.

Carefully pour the remaining cheesecake batter over the swirled layer.

Drizzle the remaining raspberry swirl over the top and create additional swirls with a knife or skewer.

Place the foil-wrapped springform pan into a large roasting pan. Carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan. This creates a water bath, which helps the cheesecake bake evenly and prevents cracking.

Carefully transfer the roasting pan with the cheesecake to the preheated oven (325°F/160°C).

Bake for 60-70 minutes, or until the edges are set, but the center 2-3 inches still jiggles slightly when gently shaken.

Turn off the oven, crack the door open slightly, and leave the cheesecake in the water bath for 1 hour to cool slowly. This also helps prevent cracks.

After 1 hour, carefully remove the cheesecake from the water bath and remove the foil. Let it cool completely on a wire rack at room temperature for another 1-2 hours.

Once completely cool, cover the cheesecake loosely with plastic wrap and refrigerate for at least 6-8 hours, or preferably overnight, before serving. Chilling is crucial for the cheesecake to set properly and develop its full flavor and creamy texture.

Before serving, carefully run a thin knife around the edge of the cheesecake to loosen it from the pan. Release and remove the springform pan sides.

Slice with a warm, clean knife for best results. Garnish with fresh raspberries if desired.