Preheat the oven to 200°C fan-forced (or 210°C conventional). Position the oven rack in the middle or slightly lower-middle of the oven.
Line a 23cm springform tin with baking paper, allowing the paper to extend above the rim of the tin for the classic rustic Basque cheesecake look. Keep the paper crinkled, but avoid it flaring too dramatically outward.
In a large mixing bowl, beat the cream cheese and caster sugar until completely smooth and creamy, scraping down the sides as needed.
Add the eggs one at a time, beating well after each addition until fully incorporated.
Add the vanilla extract (if using) and mix briefly.
Pour in the cream and mix until smooth.
Sift in the plain flour and fold or mix gently until just incorporated. Avoid overmixing.
Pour the batter into the prepared tin and tap the tin gently on the bench once or twice to release any large air bubbles.
Bake for 40–48 minutes, checking from 38 minutes.
The cheesecake is ready when:
the top is a deep mahogany brown
the edges are puffed and set
the centre still has a noticeable wobble (approximately a 7–10cm soft centre)
Remove from the oven and allow the cheesecake to cool completely in the tin. It will deflate as it cools — this is exactly what you want.
Chill for at least 4 hours, preferably overnight, before slicing.