Preheat oven to 350 degrees F. Spray a 10-inch cheesecake pan with cooking spray.
Prepare the graham cracker crust. Combine the graham cracker crumbs with melted butter and brown sugar until well combined. Pour the mixture into the prepared pan and press the crumbs into the pan and up the sides to create a crust. Bake the crust for 10 minutes or until golden brown. Remove from the oven and let cool completely.
Make the filling. Combine the cold water with vanilla and lemon juice in a small bowl. Sprinkle the gelatin on top, stirring to combine. Set aside.
Add the Greek yogurt, ¾ cup heavy cream, and the powdered sugar in the bowl of a stand mixer. Use the whisk attachment and whip the mixture until medium peaks form, about 2-3 minutes.
Combine the remaining ¼ cup heavy cream with the white chocolate in a medium bowl. Melt the white chocolate in the microwave, stirring every 20 seconds until the white chocolate is fully melted. Let cool slightly.
Heat the gelatin mix in the microwave for 10-15 seconds or until it melts and becomes liquid. While the mixing is running, slowly add the gelatin mix to the yogurt until fully incorporated. Continue to whip the yogurt and heavy cream until stiff peaks form. Fold in the white chocolate mixture until fully combined. Pour the filling into the cooled crust, cover, and chill in the fridge for at least 4 hours or overnight.
Meanwhile, make the raspberry sauce. Combine the raspberries, ¼ cup water, and sugar in a medium saucepot. Bring the mixture to a boil over high heat. Reduce the heat to low and continue to simmer for 5 minutes or until the raspberries soften and the sugar has dissolved. Remove the sauce from heat and transfer to a blender. Puree the sauce until smooth, then pour through a strainer, discarding the seeds.
Pour the sauce back into the saucepot and bring it back to a simmer over low heat. Combine the cornstarch and water in a small bowl mixing until the cornstarch has dissolved. Add the mixture to the sauce and simmer until thickened, about 2 minutes. Remove from heat and let cool completely.
Top the cheesecake with fresh berries and serve with raspberry sauce.