Melt the unsalted butter in the microwave (about 40 seconds). Add the melted butter, vanilla extract (if using), and room-temperature milk to the beaten egg. Mix well with the whisk. Add sugar and salt, whisk until fully dissolved.
Sift the flour and baking powder into the mixture. Gently fold with a whisk until no dry flour remains. Do not overmix – the bread will become dense.
Tap the mixing bowl gently to remove air bubbles from the batter.
Pour the batter into the loaf pans, filling about 1/3 of the pan height.
Crack two eggs on top of the batter.
Sprinkle a pinch of salt and add 1 tablespoon of mozzarella cheese.
Bake in the oven or air fryer at 170°C for 25 minutes. Temperatures may vary depending on your device, so adjust according to your appliance.