Melt the butter in a pot or a microwave, and set it aside. In a bowl, sift the all-purpose flour, baking powder, and salt together.
In a stand mixer with the whisk attachment, whip up the whole eggs (not salted egg yolks) and caster sugar until it turns fluffy and has doubled in volume. This will take 3-5 minutes on a medium-high speed. Then, mash up your salted egg yolks and add it in. (It’s okay if the salted egg yolk isn’t mashed till completely smooth, it’ll add some texture to the end product!). Next, stream in the melted butter and whisk it for another 2 minutes. (It’s okay if the butter is still warm, as long as it isn’t scalding.) Then, fold in the dry ingredients in 2-3 incorporations. Don’t overmix the batter; once you don’t see any streaks of flour remaining, it’s done.
Heat the oven to 165°C (convection oven). Prepare a cake tin or a bundt pan and grease it lightly. Then, pour the cake batter into the cake tin. Give it a few taps on your tabletop to release any trapped air bubbles. Then, bake it in the oven for around 1 hour and 15 minutes, or until a cake tester poked into it comes out clean. When done, let the cake cool on the wire rack for 10 minutes before unmolding.