Preheat your oven to 150°C and line an 18 cm square cake pan with parchment paper.
Sift the flour into a mixing bowl.
In a small saucepan, warm the butter and milk together until just heated, then pour this mixture into the flour and stir to combine.
Add the egg yolks and vanilla extract, mixing until smooth and creamy, then set aside.
In a separate bowl, use an electric beater to whisk the egg whites until frothy.
Gradually add the sugar while continuing to beat until the mixture becomes fluffy and forms soft peaks.
Gently fold the egg yolk mixture into the whipped egg whites, being careful not to deflate the batter.
Pour the batter into the prepared cake pan and smooth the top.
Place this pan inside a larger baking tray, pour hot boiling water into the outer tray to create a water bath, and bake for 30 to 35 minutes.
Once done, let it cool in the pan for 2 minutes, then remove the cake, unwrap the parchment paper, slice, and serve.