Prepare the crust: In a mixing bowl, combine the Graham cracker crumbs, ⅓ cup sugar, and melted butter. Mix well until the crumbs are evenly blended and moisture is absorbed. Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust. Bake in a preheated oven at 350°F (175°C) for 10 minutes, then remove and allow to cool.

Make the filling: In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add in 1 cup of sugar and mix until creamy. Add sour cream and vanilla extract, and blend until well combined.

Add the eggs: Beat in the eggs one at a time, ensuring each one is fully incorporated before adding the next. If desired, add cornstarch to thicken the mixture slightly.

Fold in the fruits: Gently fold in the diced peaches and raspberries, being careful not to crush the raspberries too much.

Combine with the crust: Pour the cream cheese filling over the pre-baked crust, smoothing the top with a spatula.

Bake the cheesecake: Bake in the oven for 50-60 minutes or until the center is set and a slight jiggle remains. Turn off the oven and let it cool for an hour with the door slightly ajar.

Chill: Refrigerate for at least 4 hours, preferably overnight, to let the flavors meld together and the cheesecake firm up.

Serve: Garnish with additional fresh fruits or a drizzle of caramel sauce if desired. Slice, serve, and enjoy the summer bliss!