Preheat the oven to 200° C (390° F).
Line your 23 cm (9") springform cake tin with parchment paper. Make sure that all the edges of the pan are covered by parchment paper.
Place the cream cheese and powdered sugar in a bowl and whisk together until fluffy. I prefer using my kitchen aid for this stage but you can also use a hand-held mixer.
Add the eggs, one at a time, and keep whisking until nicely combined.
Sift the flour and add it to the mixture along with the salt, heavy cream, and vanilla, and beat just enough to combine without overmixing it at that stage. We don't want to incorporate too much air into the cheesecake, we just want to mix it until it is smooth.
Scrape down the sides of the bowl and give it one last good mix until everything is fully mixed.
Pour the mixture into your prepared cake tin, knock the cake tin on the countertop a few times to remove any air bubbles, then put it into the preheated oven.
Bake it for 35 to 40 minutes, until the top is dark brown, the edges are set, and the middle is still very wobbly. It will firm up as the cheesecake cools. The top should end up somewhere between milk chocolate and dark chocolate in color.
Remove it from the oven and let your Basque Cheesecake cool down to room temperature.
You can serve the cheesecake at room temperature if you like the center slightly creamy and custardy, or refrigerate it for at least 4 hours, ideally overnight, if you want it firmer.