In the medium bowl of an electric mixer, beat together softened cream cheese with sugar and vanilla until smooth and creamy.
Mix in sour cream and corn starch.
Add slightly beaten eggs and mix on low just to combine; do not overmix the batter.
Pour half of the mixture (about 2-½ cups) over the crust and smooth the top.
Place springform pan in a large roasting pan; pour hot water into the roasting pan until it reaches halfway up the springform pan.
Place in the pre-heated oven and bake 13 to 15 minutes or until the top is set.
Turn down the oven temperature to 350°F.
Remove the pan from the oven and arrange thin layer of peaches over cheesecake layer; save leftover peaches (use in cobbler topping) and sauce (use when serving).
Spoon remaining cheesecake layer over the peaches; smooth the top; place back in the oven.
Bake about 40 to 45 minutes until the cheesecake is just slightly jiggly in the center.