Preheat the oven to 220°C (430°F) and set the rack to middle position.
Line a 5 inch wide by 3 inch high cake pan with parchment paper or use a non stick pan and set aside.
Add the cream cheese and sugar into a medium size bowl and stir using a whisk until the cream cheese mixture is soft and smooth about 2-3 minutes. You can also use a hand beater or planetary mixer with the paddle attachment and mix on medium speed.
Add into the cream cheese mixture the egg yolk and mix until well combined followed by adding one whole egg at a time, mixing until the mixture is creamy and smooth.
Lastly add the cake flour and mix until well combined.
Transfer the cream cheese cake batter into 5X3 inch baking pan and bang it on your counter 2 to 3 times to even out the surface and remove any air bubbles.
Place into pre-heated oven and bake for 25-30 minutes.
Remove the burnt cheesecake from the oven, the cheesecake will be jiggly, let it cool in the pan for approximately 20 minutes, then refrigerate overnight.
Unwrap the parchment from the Basque cheesecake, slice and serve.
Enjoy as is or dusted with icing sugar, you can also serve with fresh berries and fruit or spread a strawberry or blueberry jam onto top.