Heat the oven to 175 °C or 350 °F, line an 8-inch cake tin with baking paper, and prepare a 7-inch cake tin that is 4 inches high with baking paper on the base and acetate around the sides. The acetate helps the mousse set with smooth edges and makes unmolding much cleaner later.

Warm the milk and butter together in a small bowl in the microwave for about 30 seconds, then leave the mixture aside to cool. The butter should be fully melted, and the bowl should no longer feel hot before it goes near the whipped eggs.

Beat the eggs, caster sugar, and vanilla extract in a large bowl with electric beaters until the mixture turns pale and expands to roughly triple its starting volume. It should look thick and airy, and ribbons should briefly sit on the surface before sinking back.

Sift in the matcha tea powder and all-purpose flour, then fold gently with a spatula until the dry pockets disappear. The batter should stay fluffy and evenly green without streaks of flour hiding at the bottom.

Pour the cooled milk mixture down the side of the bowl and fold only until incorporated. Stop as soon as the batter looks smooth, because over-mixing will knock out the volume that keeps the sponge light.

Transfer the batter to the lined 8-inch tin and bake for 15 to 20 minutes. The sponge should spring back lightly when touched and keep a soft, even surface.

Cut the baked sponge with a 7-inch cutter and place the trimmed round inside the lined 7-inch tin. Brush or wipe away loose crumbs from the acetate so dark specks do not show through the white mousse.

Place all 9 gelatin leaves in a large bowl of cold water so they can soften while you prepare the mousse bases. The leaves should become flexible and slippery instead of stiff.

Whisk the cold water, 1/4 cup of the cream, and the melted white chocolate in a microwave-safe bowl, then heat the mixture for 90 seconds. The mixture should look fluid and glossy rather than thick or clumpy.

Lift 6 softened gelatin leaves from the water, squeeze out the excess, and whisk them into the warm white chocolate mixture one at a time. Each piece should dissolve before the next goes in so you do not end up with gelatin bits in the final mousse.

Let the white chocolate mixture cool to room temperature before moving on. It should still pour easily but feel cool enough that it will not collapse the whipped cream.

Whip the remaining cream with powdered sugar and vanilla extract to stiff peaks, then fold the cooled white chocolate mixture in gently. The mousse should hold soft ridges and look thick, smooth, and airy.

Spoon the mousse over the sponge in the 7-inch tin and smooth the top evenly. The surface should level neatly with a spatula and sit in a thick, stable layer.

Refrigerate the cake until the white chocolate layer is set enough to support the next mousse. A gentle shake should show only a slight wobble in the center, not a loose wave across the whole layer.

Whisk the cold water, 100ml cream, and matcha tea powder in a microwave-safe bowl, then microwave for 90 seconds. The mixture should turn smooth and deep green with no dry matcha clinging to the edges.

Squeeze the water from the remaining 3 gelatin leaves and whisk them into the warm matcha mixture, then cool it to room temperature. The base should look glossy and fluid, not hot, thick, or grainy.

Whip the remaining cream with powdered sugar and vanilla to stiff peaks, then fold in the cooled matcha mixture gently. The mousse should look evenly green and airy, with enough body to mound lightly on the spatula.

Spoon the matcha mousse over the chilled white chocolate layer and smooth the top. The layer should spread without sinking into the mousse below if the first layer is properly set.

Freeze the assembled cake for 4 hours, then lift it from the tin, dust the top with matcha powder, remove the acetate, slice, and serve. The cake should feel firm enough to cut cleanly, with distinct layers visible from top to bottom.