In a small saucepan, stir to combine the raspberries, granulated sugar, and lemon juice. Cook over medium heat, stirring frequently to break up the raspberries, for 8 to 10 minutes, until bubbling and saucy. Reduce the heat to low.

In a small bowl, whisk the cornstarch into 1 tablespoon of water until completely dissolved.

While stirring the raspberry sauce, pour in the cornstarch mixture and stir well to combine. Increase the heat to medium and allow the mixture to return to a simmer. Cook for 1 to 2 minutes, until slightly thickened. Remove from the heat.

Immediately strain the sauce through a fine mesh strainer. Stir vigorously with a spoon to push the sauce through the sieve and remove the seeds. Set the sauce aside to cool to room temperature.

Preheat the oven to 350°F. Spray a 9-inch springform pan with nonstick spray.

In a medium bowl, stir to combine the graham cracker crumbs, 6 tablespoons melted butter, sugar, and salt until the mixture looks like wet sand and holds together when pinched. (If the mixture feels dry or loses shape when released from the pinch, stir in more melted butter 1 tablespoon at a time, up to 2 tablespoons.)

Pour the crust mixture into the prepared springform pan. Using a flat-bottomed glass or measuring cup, press the crumbs into an even layer along the bottom and 1½ to 2 inches up the side of the pan.

Bake for 10 to 12 minutes or until lightly golden and aromatic. Let cool on a wire rack while you make the filling.

Place the cream cheese and sugar in a large mixing bowl or the bowl of a stand mixer with the paddle attachment. Beat on medium-low speed until creamy and smooth, about 2 minutes. Add the sour cream, salt, and vanilla. Beat on low until the mixture is combined, then increase to medium-low and beat until the mixture is completely smooth.

Add the eggs one at a time, beating on low speed until fully combined between each addition. Scrape down the sides and bottom of the bowl as needed.

Pour about half the batter into the cooled crust and spread it into an even layer. Drizzle ¼ cup of the raspberry sauce evenly over the batter. Swirl with a toothpick or wooden skewer.

Gently pour the remaining batter over the top, starting at the edges and pouring in a circular motion towards the center. Drizzle another ¼ cup of the raspberry sauce evenly over the batter. Swirl just the surface with the wooden skewer.

Bake for 15 minutes. Reduce the oven temperature to 300°F and continue baking for another 30 to 35 minutes or until the edges of the filling are just slightly puffed and the center wobbles lightly when gently shaken.

Turn off the oven and leave the cheesecake in the oven with the door closed for 1 hour. Remove the cheesecake and let cool at room temperature for another hour, then refrigerate for at least 6 hours or up to 3 days before serving.

Serve with extra fresh raspberries and a drizzle of the remaining sauce, if you like.