Preheat the oven to the 450°F (230°C).
Line a 6-inch cake pan with 2.5-inch sides with parchment paper. If the pan has a removable bottom, you can use the bottom to press the paper into the pan. Then you can use your hands to crease the sides to hold its shape. Once the paper is molded to the pan, you can remove the bottom and the paper and then reattach the bottom to the pan, placing the paper on top.
Add 226 grams cream cheese, 1 cup heavy cream, 100 grams granulated sugar, 2 large eggs, 15 grams cake flour, and ½ teaspoon vanilla extract to a blender and blend until smooth. I usually let this mixture rest for about 20 minutes to give the air bubbles in the batter a chance to settle, but you can bake it right away if you're in a rush.
226 grams cream cheese, 1 cup heavy cream, 100 grams granulated sugar, 2 large eggs, 15 grams cake flour, ½ teaspoon vanilla extract
Pour the mixture into the prepared pan and then drop the pan a few times onto a kitchen towel to coax any remaining bubbles out of the batter.
Bake the cheesecake until the top is just shy of turning black. This takes 22 minutes in my oven but this will vary on your oven (see headnotes above for more information). The cake should still be very jiggly in the center when you remove it from the oven.
Let the burnt cheesecake cool on a cooling rack and then place it in a sealable bag and refrigerate overnight.
To slice the Basque Cheesecake, prepare a long sharp knife along with a pot of boiling water. Clean and heat the knife with the hot water between each slice. This ensures you get nice clean slices.