In a large bowl, put the cream cheese, and beat with an electric whisk on a low speed until soft, smooth, and spreadable.
Add the sugar, and beat on a low speed until the grains of sugar have dissolved.
Add eggs one at a time, beating for 15 seconds before adding the next.
Using a fine-mesh strainer, sift flour over the batter. Beat on low speed until combined around 20 seconds. Then pour in the cream, and beat until smooth and creamy.
Pour the cake mix into the 18 cm tin lined with parchment paper.
Bake in a preheated oven at 210 C(410 F) for 35 minutes. The middle will still be wobbly and slightly liquid. The cheesecake should be deeply caramelized on the outside.
Remove from the oven, leave to cool in the pan on a wire rack at room temperature for 1 hour, and then refrigerate overnight.
Gently peel back parchment paper from the sides of the cheesecake, and use a knife to cut it into wedges.
Serve chilled or allow the cheesecake to come to room temperature before serving.
Notes
Use Caster Sugar: I suggest using caster sugar because it dissolves more easily in the batter.Keep the ingredients at Room Temperature:To keep the batter smooth and lump-free, mix everything evenly, but be careful not to over-stir.Use an Electric Hand Mixer: It's helpful to use a whisk to mix all the ingredients together. If you don't have a whisk, that's okay too.Do Not Overbake: The center should still be jiggly when you take it out of the oven. It will firm up as it cools.Cool Completely: Let it cool completely in the pan before removing. For the best texture, refrigerate for a few hours or overnight.Serve at Room Temperature: Serve Basque cheesecake at room temperature for the creamiest texture and best flavor.