Line the base of a 9-inch springform pan with parchment. Stir together the graham-cracker crumbs, melted butter, granulated sugar, and salt, then press the mixture firmly over the bottom and slightly up the sides of the pan. Refrigerate the crust while preparing the other components.

Heat the oven to 400°F (200°C). Toss the chopped peaches with brown sugar, lemon juice, vanilla, bourbon if using, and salt, then spread them on a parchment-lined baking sheet and roast for 20–30 minutes, until softened, bubbling, and lightly caramelized.

Scrape the roasted peaches and all their juices into a saucepan or bowl. Mash or briefly blend the fruit until chunky or mostly smooth, according to your preference, then cool completely; refrigerate it if needed because the jam thickens as it cools.

Beat the softened cream cheese until smooth. Add the confectioners’ sugar, vanilla, and lemon juice, and continue beating until the mixture is creamy and free of lumps.

Whip the cold heavy cream in a separate chilled bowl to medium-stiff peaks. Fold the whipped cream gently into the cream-cheese mixture in two or three additions, stopping as soon as the filling is combined.

Spread about half of the cheesecake filling over the chilled crust. Spoon in some peach jam and swirl it lightly with a knife, then add the remaining filling and smooth the top.

Spoon the remaining peach jam over the surface and use a knife to make decorative swirls. Cover the pan and refrigerate for at least 4 hours, preferably overnight, before serving chilled.

Release the springform ring while the cheesecake is cold. For especially neat slices, dip a knife in hot water, wipe it dry, and repeat before each cut.