Begin by crushing the graham crackers into fine crumbs using a food processor. Combine the graham cracker crumbs with granulated sugar and melted salted butter, mixing until the mixture resembles wet sand. Press this mixture firmly into the bottom and up the sides of a 9-inch springform pan, creating an even layer. Chill the crust in the freezer for about 10-15 minutes to set.

While the crust is chilling, blend two cans of drained peaches until smooth, reserving 1 cup for later. In a large mixing bowl, beat the softened cream cheese with granulated sugar until creamy and smooth. Gradually fold in the peach puree, fresh lemon juice, and vanilla extract until fully incorporated. Gently fold in the frozen whipped topping to create a light and airy filling.

Once the filling is ready, remove the crust from the freezer. Pour the peach cheesecake filling into the prepared crust, smoothing the top with a spatula. Cover the cheesecake with plastic wrap and refrigerate for at least 4-6 hours, or overnight, to allow it to set properly and achieve the desired creamy texture.

To make the topping, heat the reserved peach puree in a saucepan over medium heat until it begins to simmer. In a small bowl, mix cornstarch with a bit of lemon juice to create a slurry, then whisk it into the simmering peach mixture. Add chopped fresh peaches, if desired, and cook until the mixture thickens, about 2-3 minutes. Set the topping aside to cool completely.

Once the No Bake Peach Cheesecake has fully set, carefully remove it from the springform pan. Spoon the chilled peach topping over the cheesecake and garnish with additional whipped cream if you like. Using a warmed knife allows for clean slices, making it easier to serve this delectable dessert at your next gathering.