Preheat your oven to 160°C (320°F). Line the bottom of a 9-inch round cake pan with baking paper and lightly grease the sides.
In a mixing bowl, combine softened cream cheese, melted butter, and miso paste. Whisk until smooth and creamy, with no lumps remaining.
Add milk to the mixture and stir until fully incorporated. Then mix in the caster sugar and vanilla extract until the sugar dissolves completely.
Sift the flour into the bowl and gently fold it in with a silicone spatula, avoiding deflating the mixture. Set aside.
In a clean, dry bowl, add egg whites and cream of tartar. Whisk with an electric mixer until stiff, glossy peaks form, and the whites are firm but not dry.
Carefully fold a third of the whipped egg whites into the batter to loosen it, then gently fold in the remaining whites until just combined and smooth.
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Tap the pan gently on the counter to release any air bubbles.
Bake in the preheated oven for about 35 minutes, until the cake is puffed, lightly golden on top, and a toothpick inserted in the center comes out clean.
Remove from the oven and allow the cake to cool in the pan for 10 minutes. Then, transfer it to a wire rack to cool completely—this helps prevent shrinking.
Once cooled, gently release the cake from the pan, remove the parchment paper, and serve slices that are tender, airy, and melt-in-your-mouth soft.