Preheat the oven to 425°F / 220°C and line an 8-inch cake pan with two pieces of parchment paper. There is no need for any grease or spray, and the paper does not need to be neat.
Beat the sugar and cream cheese together on medium speed until smooth and combined.
3 cups Cream Cheese, 1 cup White Sugar
Add eggs, one at a time, beating in between each addition. Add the egg yolk in the same way.
4 Eggs, 1 Egg Yolk
In a separate bowl, mix together the cake flour and a small splash of the cream, mix until the flour turns into a paste, then gradually add the rest of the cream, stirring the whole time.
¼ cup Cake Flour, 1 ⅔ cups Heavy Cream
Gradually add the cream mixture to the cream cheese mixture, stirring as you go. Mix well until everything is combined and there are no lumps.
Pour the cheesecake mixture into the prepared cake pan and tap it on the counter a few times to release any big air bubbles.
Put the cheesecake on the middle rack of the oven and bake for 35-45 minutes or until the edges are set but the inside is still wobbly. The top of the cheesecake should go dark brown or even black in some places - this is good!
Remove from the oven and let the cheesecake cool on the countertop completely. As it cools, it will sink slightly and may even crack - don't worry this is all part of the rustic charm of this cheesecake!
For the classic San Sebastian cheesecake with a soft, custardy center, serve it at room temperature without chilling. For a firmer, more set cheesecake, chill it first for at least 2 hours before serving.
Notes
Make sure your cream cheese, eggs, and heavy cream are all at room temperature before beginning to bake. This will ensure that they incorporate properly and you won't have any lumps. Some people like to add a little vanilla and lemon zest to this recipe to give it some extra lift. Personally, I like the classic recipe as it is, but if you'd like to add these flavorings, add them in after the eggs and before the cream.