Preheat the oven to 175C / 350F. Grease and line a 23x33 cm / 9x13-inch baking pan with parchment, leaving overhang on two sides.

In a large mixing bowl, whisk the eggs and sugar with a hand mixer for 3 to 4 minutes until pale, thick, and doubled in volume.

Warm the milk and 50 g butter in a small saucepan over low heat until the butter melts and the mixture feels warm, not hot. Stir in the vanilla.

Sift the flour, baking powder, and salt over the egg mixture. Fold gently with a rubber spatula until just combined.

Pour the warm milk mixture down the side of the bowl and fold until the batter is smooth with no streaks.

Pour the batter into the prepared pan and spread evenly. Bake for 25 to 30 minutes until a toothpick inserted in the center comes out clean and the top springs back lightly.

While the cake bakes, combine the topping butter, brown sugar, and 60 ml milk in a 2-quart / 1.9 L saucepan over medium heat. Stir for 3 to 4 minutes until the sugar dissolves and the mixture is smooth. Remove from heat and stir in the coconut.

Remove the cake from the oven and switch the oven to broil. Spread the topping evenly over the hot cake while it's still in the pan.

Broil for 3 to 5 minutes, watching closely, until the topping bubbles and turns deep golden brown. Don't walk away, it can burn in under a minute once it starts browning.

Cool the cake in the pan on a wire rack for at least 15 minutes before lifting it out by the parchment overhang and slicing into 12 squares.