Preheat oven to 350°F (175°C). Line an 8x8-inch pan with parchment paper. Combine graham cracker crumbs, sugar, and melted butter. Press into the bottom of the pan and bake for 10 minutes.

Beat room temperature cream cheese until smooth. Add sugar, then beat in eggs one at a time on low speed. Stir in sour cream and vanilla.

Pour filling over the crust. Bake for 30-35 minutes until the center is just set. Turn off the oven and let it cool inside with the door ajar for 1 hour.

To make the caramel, cook sugar and water in a saucepan until it turns an amber color. Carefully whisk in warm heavy cream, then add butter and miso paste, whisking until smooth. Let cool until thickened.

Pour the cooled caramel over the cheesecake. Refrigerate for at least 4 hours or overnight before lifting out of the pan and slicing.