Sift the flour and baking powder, add them gradually to the mixture while stirring carefully with a spoon.
Pour the mixture into a suitable buttered tray and bake in a preheated 356°F (180 °C) oven about 30 min. My tray measures 9 1/2″ (24 cm) x 6 1/4″ (16 cm) but if yours is wider, your cake will be thinner and therefore take less time to bake - check with a toothpick after the 20th minute.
Leave the ready cake to cool while you make the syrup. First, melt the butter on low heat with the milk, then add the cocoa and vanilla, stir well. Boil until slightly thickened, then pour it over the cooled cake.
After it cools a bit, melt the butter for the couverture in a small container with the milk on very low heat. Crumble the white chocolate into it and once it melts too, distribute it over the cake in a thin trickle, drawing figures or just stripes, for a beautiful combination of milk and white chocolate.
Cover with a clean towel and let sit for at least 1 hour. Then consume with delight.