
Peel the peaches using a vegetable peeler, then chop them into small pieces (about 1 centimeter cubes). Add chopped peaches to a mixing bowl and toss them with the granulated sugar and lemon zest. Set aside.
In a large mixing bowl, combine the cold heavy whipping cream, powdered sugar, vanilla extract, and salt. Using an electric mixer, beat on medium-high speed until stiff peaks form. Be careful not to overbeat, or it will turn into butter.
Use a rubber spatula to spread 1 cup of the whipped cream evenly over the bottom of springform pan.
Arrange a single layer of graham crackers over the whipped cream, breaking them as needed to fit. Don't worry if there are small gaps.
Spread 1/3 of the chopped peaches over the whipped cream.
Repeat the layers twice more: 1 cup whipped cream, graham crackers, peaches. Finish with a final layer of the remaining whipped cream on top.
Cover the pan tightly with plastic wrap. Refrigerate for at least 6 hours, or preferably overnight. This allows the graham crackers to soften, creating a cake-like consistency.
About 30 minutes before serving the cake, slice the remaining peaches and add them to a mixing bowl with the granulated sugar. Toss to combine.
Remove the chilled cake from the refrigerator and place it on a cake stand or serving platter. Remove the top piece of plastic wrap. Run a paring knife along the inside of the inside edge of the springform pan. Remove the side of the springform pan.
Top with a big pile of the peaches and lemon zest. Slice and serve immediately.
Store leftover cake in an airtight container in the refrigerator for up to 3 days. The graham crackers will continue to soften over time.