Preheat your oven to 180°C (350°F). Line a baking tray with parchment paper.
In a mixing bowl, beat the eggs and sugar until light and fluffy.
Sift the flour and matcha powder together, then fold into the egg mixture.
Add the milk and vanilla extract, and mix until smooth.
Pour the batter into the prepared baking tray and spread evenly.
Bake for 12-15 minutes, or until a toothpick inserted comes out clean.
Let the cake cool slightly, then roll it up with the parchment paper and let it cool completely.
Whip the heavy cream and sugar together until stiff peaks form.
Unroll the cake, spread the whipped cream evenly, and roll it back up.
Chill in the fridge for at least an hour before serving.