Combine graham crackers, granulated sugar, and melted butter in a food processor. Pulse until the mixture resembles wet sand, about 30 seconds. Pour into a 9-inch springform pan, pressing firmly across the bottom. Chill in the refrigerator for at least 30 minutes.

In a blender, puree two cans of drained peach slices until smooth, about 1 minute. Measure out 1 cup for filling. In a mixing bowl, beat room-temperature cream cheese and sugar until smooth, 2-3 minutes. Add 1 cup peach puree, lemon juice, and vanilla, blending until well combined.

Gently fold in the frozen whipped topping into the peach-infused cream cheese mixture using a spatula to retain light and airy texture. Once combined, the filling should appear fluffy and vibrant.

Pour the cream cheese mixture over the chilled crust in the springform pan. Spread the filling evenly and smooth the top. Cover with plastic wrap and refrigerate for 4 to 6 hours, or overnight until set.

To create the topping, combine remaining peach puree and granulated sugar in a saucepan over medium heat. Whisk cornstarch with lemon juice in a separate bowl until smooth, then add to the saucepan, stirring continuously. Simmer for about 2-3 minutes until thickened and glossy, then cool completely.

Carefully remove the cheesecake from the springform pan. Spread the cooled peach mixture evenly on top, letting it cascade over the edges. Garnish with dollops of whipped cream before slicing and serving.