In a large mixing bowl, combine the sifted matcha powder and cornstarch. Whisk them together until evenly distributed and no lumps of matcha remain.

Add the whole egg and granulated sugar to the bowl. Pour in the milk. Whisk until everything is fully incorporated and you have a smooth, thin, pale green liquid.

Place a fine-mesh sieve over a medium-sized saucepan. Pour the matcha-milk mixture through the sieve into the pan to catch any potential lumps.

Place the saucepan over medium-low heat. Cook, stirring constantly and scraping the bottom and sides of the pan with a silicone spatula.

After a few minutes, the mixture will begin to thicken.

Continue stirring until it becomes very thick and pudding-like, and leaves a clear trail on the back of the spatula that doesn't immediately drip away. This should take about 8-10 minutes total. Once thickened, immediately remove from heat.

Quickly pour the hot, thickened custard into your desired container or mold (a small glass or ceramic baking dish, or individual ramekins work well). Smooth the top with the spatula.

Gently tap the container on the counter a few times to release any trapped air bubbles.

Cover with plastic wrap and lightly press the surface flat with your hand. Let it cool to room temperature on the counter, then transfer to the refrigerator. Chill for at least 4 hours, but preferably overnight, to allow it to set completely and become firm enough to slice.

The next day, line a small baking sheet with parchment paper.

Remove the set custard from the fridge. Invert it onto a cutting board—it should release cleanly. Using a sharp knife, cut it into your desired shapes (squares, rectangles, or triangles).

Place the pieces on the prepared baking sheet, spaced slightly apart. Lightly brush the top each piece with the beaten egg yolk. This will give them a beautiful, glossy, deep golden color when baked.

Place the cake pieces on the middle rack and bake at 180°C (356°F) for 18 minutes, until the surface is golden and lightly crisp.