Whisk 1 egg, 40g sugar, salt, and vanilla in a saucepan, then mix in 1 tbsp cornstarch until smooth. Add 200ml warm milk, cook until thickened, stir in 1 tbsp butter, and let it cool.
Sift 240g all-purpose flour, 2 tsp baking powder, and 1/4 tsp salt in a bowl. Whisk to combine evenly.
Beat 2 eggs, 80g sugar, and 1 tsp vanilla extract until frothy. Mix in 2 tbsp melted butter or oil.
Gradually mix dry ingredients into wet ingredients in two parts, adding 150ml milk in between. Stir gently until just combined and let rest.
Slice 2–3 ripe bananas and arrange them at the bottom of a greased and parchment-lined 23 x 23cm (9 x 9 inch) pan.
Pour the batter over the bananas, smooth the top, and pipe cooled custard in a lattice pattern on top.
Bake at 180°C (356°F) for 35–40 minutes until golden and a toothpick comes out clean.
Let the cake cool slightly, then remove it from the pan and dust it with powdered sugar before slicing and serving.