Step 1: Preheat your oven to 350°F (175°C). Wrap the bottom of a 9-inch springform pan tightly with heavy-duty aluminum foil to prevent any water bath leakage.
Step 2: In a medium bowl, combine 1 ½ cups of graham cracker crumbs with ¼ cup granulated sugar. Pour in 6 tablespoons of melted unsalted butter and mix until the crumbs are evenly moistened.
Step 3: Press the mixture firmly and evenly into the bottom of the prepared springform pan. Use the bottom of a flat glass or measuring cup to get a compact, uniform crust.
Step 4: Bake for 8-10 minutes, or until lightly golden. Remove from oven and let cool slightly while you prepare the filling.
Step 5: Reduce oven temperature to 325°F (160°C).
Step 6: In a large mixing bowl, beat four (8-ounce) packages of full-fat cream cheese (at room temperature) with 1 cup granulated sugar on medium speed until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Step 7: Beat in ½ cup sour cream (at room temperature) and 2 tablespoons yuzu juice until just combined. Be careful not to overmix at this stage.
Step 8: Add 1 teaspoon vanilla extract. Then, one at a time, beat in 4 large eggs (at room temperature), mixing on low speed until just incorporated after each addition. Overmixing eggs can introduce too much air, leading to cracks.
Step 9: Gently fold in ¼ cup passionfruit purée (strained if you prefer it smooth). You want swirls of passionfruit, not a fully homogenous mixture, to create a beautiful marbling effect.
Step 10: Pour the cheesecake filling over the cooled graham cracker crust in the springform pan.
Step 11: Place the springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan.
Step 12: Bake for 60-75 minutes, or until the edges are set but the center still jiggles slightly when gently shaken.
Step 13: Turn off the oven, crack the oven door open, and let the cheesecake cool in the water bath for 1 hour. This slow cooling prevents drastic temperature changes that can cause cracks.
Step 14: Carefully remove the cheesecake from the water bath, remove the foil, and transfer it to a wire rack to cool completely at room temperature for another 1-2 hours.
Step 15: Once cool, cover the cheesecake loosely with plastic wrap and refrigerate for at least 6 hours, or preferably overnight. Chilling is essential for the cheesecake to fully set and develop its flavor.
Step 16: For the optional glaze: In a small saucepan, combine ½ cup passionfruit purée, 2 tablespoons granulated sugar, and 1 tablespoon cornstarch. Whisk until smooth.
Step 17: Heat over medium heat, stirring constantly, until the mixture thickens and comes to a gentle boil. Cook for 1 minute, then remove from heat.
Step 18: Stir in an additional 1-2 tablespoons of yuzu juice for an extra zing. Let the glaze cool completely to room temperature before pouring it over the chilled cheesecake.
Step 19: Carefully spread the glaze evenly over the top of the cheesecake. Return to the refrigerator for at least 30 minutes to allow the glaze to set.