Preheat your oven to 350°F (175°C). In a medium bowl, combine graham cracker crumbs, melted unsalted butter, and granulated sugar until well mixed. Press this mixture firmly into the bottom of a 9-inch springform pan, creating an even layer. Bake for 8-10 minutes, or until the crust is lightly golden and fragrant. Once done, remove from the oven and let it cool completely.

In a saucepan over medium heat, combine hulled fresh strawberries, granulated sugar, and freshly squeezed lemon juice. Cook for about 5-7 minutes until the strawberries soften and release their juices. In a small bowl, mix cornstarch with a tablespoon of water, then stir this mixture into the strawberry mixture until thickened. For a smoother texture, puree the mixture using an immersion blender, if desired, then set aside to cool.

In a large mixing bowl, beat room-temperature cream cheese until it becomes smooth and creamy. Gradually add in the granulated sugar, mixing well. Next, add eggs and egg yolks one at a time, ensuring each is incorporated before adding the next. Then mix in vanilla extract, sour cream, and all-purpose flour until the filling is perfectly blended and fluffy.

Pour half of the cheesecake filling onto the cooled crust, smoothing it out evenly with a spatula. Dollop spoonfuls of the strawberry swirl onto the filling, then pour over the remaining cheesecake mixture. Using a knife, gently swirl the strawberry mixture into the filling to create a marbled effect, being careful not to mix it completely.

Wrap the springform pan in aluminum foil to prevent water from seeping in. Place it in a larger roasting pan and fill the outer pan with hot water until it reaches halfway up the sides of the cheesecake pan. Bake for about 55-70 minutes, or until the edges are set but the center still jiggles slightly when gently shaken.

Once baked, turn off the oven and leave the cheesecake inside with the door slightly ajar for an hour. This gentle cooling helps prevent cracks. After an hour, transfer the cheesecake to a wire rack and allow it to cool completely at room temperature. Refrigerate for at least 4 hours, or overnight, to firm up.

Carefully release the cheesecake from the springform pan. Garnish with fresh strawberries and a dollop of whipped cream, if desired. Slice with a sharp knife, wiping it clean between cuts for neat slices. Enjoy this Strawberry Swirl Cheesecake, and store any leftovers covered in the refrigerator for up to 5 days.