Preheat the Oven: Preheat the oven to 220°C / 425°F (200°C fan) with the oven shelf positioned in the middle.
Prepare the Pan: Scrunch two 40 cm / 16-inch sheets of baking/parchment paper and arrange them in an “X” inside a 20 cm / 8-inch springform pan that is about 6 cm / 2.5 inches tall. Press the paper into the corners and fold the excess over the rim. Do not grease the pan. The crumpled paper should remain rustic and pleated rather than perfectly smooth. Beat the Cream Cheese: Place the room-temperature cream cheese in a large mixing bowl and beat on medium speed for 2 minutes, scraping down the sides as needed, until completely smooth and free of lumps.
Add the Sugar: Add the caster sugar to the cream cheese and beat on low speed for 10 seconds, just until incorporated.
Make the Flour Paste: Place about one-quarter of the whipping cream in a separate medium bowl with all of the flour. Whisk by hand until the flour is completely incorporated and the mixture becomes a smooth, paste-like consistency.
Finish the Cream Mixture: Slowly whisk the remaining whipping cream into the flour mixture. Once the flour is fully incorporated, whisk in the vanilla. The finished mixture should remain pourable rather than whipped.
Combine the Cream Mixture: With the electric beater running on low speed, slowly pour the cream mixture into the cream cheese mixture. Beat only until the ingredients are combined.
Add the Eggs: Keeping the beater on low speed, slowly pour in the lightly whisked eggs. Stop mixing as soon as the eggs are incorporated to minimize the formation of air bubbles.
Fill the Pan: Pour the finished batter into the prepared springform pan.
Remove Air Bubbles: Gently bang the filled pan against the counter so air bubbles rise to the surface. Use a small sharp knife to pop any visible bubbles. Repeat this process 3–5 times.
Bake the Cheesecake: Bake for approximately 45 minutes, or until the surface becomes a deep golden brown. Depending on the oven, baking may take up to 65 minutes. Watch particularly closely during the final 15 minutes. The top should be deeply caramelized without becoming burnt, while the center should remain noticeably wobbly. The cheesecake will rise dramatically during baking, similar to a soufflé. Cool the Cheesecake: Leave the cheesecake in its pan on the counter for at least 2 hours. It will sink as it cools; this is normal.
Chill Overnight: Refrigerate the cooled cheesecake uncovered for at least 8 hours, preferably overnight.
Release the Cheesecake: Remove the sides of the springform pan. Use the excess parchment overhang to lift the cheesecake from the base onto a cutting board or serving plate, then fold the parchment sides down.
Bring to Serving Temperature: If desired, allow the chilled cheesecake to stand at room temperature for 30 minutes before serving. It can also be served chilled.
Slice and Serve: Cut the cheesecake into slices like a traditional cake and serve as it is. The creamy Basque cheesecake is designed to be enjoyed without additional cream, berries, or other toppings.