In a bowl of a stand mixer fitted with the paddle attachment (or with a handheld electric mixer), beat cream cheese and sugar on medium low speed until it forms a smooth texture and no lumps remained. Scrape down the bowl as needed. Then, mix in the sour cream (or Greek yogurt) and vanilla extract and beat until combined, scrape down the sides of the bowl if needed.
Beat in eggs, one at a time on low speed until fully incorporated. Scrape down the bowl using a rubber spatula halfway through and continue to mix until combined. After the final egg is incorporated into the batter, stop the mixer and pour half of the cool peach sauce into the batter, using a rubber spatula to gently fold the sauce into the cheesecake filling until combined. Pour the batter into the cooled graham cracker crust, give the pan a gentle shake or a few taps to even it out and bring up any bubbles, or use a rubber spatula to spread evenly, and transfer to the oven to bake.
Wrap the bottom and sides of the pan with one large piece of foil all the way up, make sure that water from the bath doesn’t seep into the cake. Place the pan inside a large roasting pan, then fill the roasting pan with boiling water until it comes about halfway up the side of the springform pan. Place gently in the oven and bake for 60-70 minutes or until the sides are set but the center is still slightly jiggly (it will set as it rests in the fridge).
Allow the cheesecake to cool at room temperature. Cover it with plastic wrap and refrigerate for at least 4 hours, preferably overnight before serving.
Cheesecake is best served cool. Serve the cheesecake with remaining peach sauce. Garnish with slices of fresh peaches (optional). Cover and store leftover cheesecake in the fridge for up to 5 days.