Basque Cheesecake

Also called a Burned Basque Cheesecake or a San Sebastian Cheesecake.

Ingredients

Preheat the oven to 425F and line an 8 inch cake pan with two pieces of parchment paper. There is no need to grease the paper and it does not need to be neat (the crinkles add character to the cheesecake).
Beat the sugar and cream cheese together on medium speed until smooth and combined.
Add eggs one at a time beating between each addition. Add the egg yolk the same way.
In a separate bowl mix together the cake flour and a splash of the cream, mix until the flour becomes a paste then gradually add the remaining cream, mixing the whole time.
Gradually add the cream mixture to the cream cheese mixture, mixing as you go. Mix well until everything is combined and there are no lumps.
Pour the cheesecake mixture into the prepared pan and tap it on the counter a few times to release any large air bubbles.
Put the cheesecake on the middle rack of the oven and bake for 35-45 minutes or until the edges are set and the inside is still wobbly. The top of the cheesecake should be dark brown or even black in some places.
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 part of the charm of this particular type of cheesecake.
For a classic Basque cheesecake with a soft custardy center, serve at room temperature without cooling. For a more firm, set cheesecake; cool for up to 2 hours before serving.

Ensure that the cream cheese, eggs, and cream are all at room temperature before starting, this will ensure that they incorporate properly and don't form lumps.
No flavorings are necessary but if you do want to add some vanilla or lemon zest then do that after adding the eggs but before adding the cream.