Step 1: Prepare the crust. In a medium bowl, combine the graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Mix until well combined. Press the mixture firmly into the bottom of a 9-inch springform pan. Place in the freezer while you prepare the filling.
Step 2: Make the filling. In a large bowl, using an electric mixer, beat the softened cream cheese until smooth and creamy. Add 1 cup granulated sugar, vanilla extract, and lemon juice. Beat until fully incorporated and smooth.
Step 3: Whip the cream. In a separate large bowl, using clean beaters, whip the cold heavy cream until stiff peaks form.
Step 4: Combine. Gently fold the whipped cream into the cream cheese mixture until no streaks remain and the filling is light and airy.
Step 5: Assemble. Pour the cheesecake filling over the chilled graham cracker crust and spread evenly. Arrange most of the peach slices decoratively over the top of the filling, reserving a few for garnish if desired.
Step 6: Chill. Cover the springform pan loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, until the cheesecake is firm and set. If you are worried about your crust getting soggy, ensure your peaches are very dry before placing them on top.
Step 7: Serve. Carefully remove the sides of the springform pan. Garnish with remaining fresh peach slices and fresh mint leaves, if using. Slice and serve cold.