Preheat the oven to 160C (320F) and line the bottom and the sides of three 6-inch cake pans (15cm) with parchment paper.

In a bowl, sift together the flour, matcha powder, baking powder, and salt. Set aside.

In a stand mixer fitted with a paddle attachment (or use a hand mixer and a bowl), add the butter and sugar and beat until pale and fluffy. Then add the oil and vanilla and beat until fully incorporated. Scrape the bottom and the sides of the bowl and beat for a few seconds.

Add the eggs one at a time and beat until emulsified.

Add the flour mixture to the butter mixture in three parts, alternating with the milk in two parts and beginning and ending with the flour mixture. Beat until just combined.

Divide the batter between the prepared pans and bake for 25-30 minutes or until a toothpick inserted in the center of the cake comes out clean. Bake in batches if needed.

Let the cakes cool in the pans for 5 minutes before transferring them to a wire rack to cool completely. Wrap tightly in the plastic wrap and store in the fridge if you’re planning to assemble the cake another day.

In a bowl, whisk together the egg yolks, salt, cornstarch, vanilla extract, and half of the sugar until smooth.

Heat the milk, matcha powder, and the rest of the sugar in a saucepan until simmering.

Pour the hot milk into the egg yolk mixture while whisking vigorously. Pour everything back into the saucepan and cook it over medium heat, whisking constantly until it thickens and becomes pudding-like in consistency.

Remove the pan from the heat and stir in the butter until it’s melted.

Transfer the mixture to a bowl and cover it with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming.

Chill the custard in the fridge until cold or use the freezer to speed up the process.

In a large bowl, whip the heavy cream until medium peaks form.

Add the chilled custard ⅓ at a time and whip into the whipped cream until well combined and stable.

In the bowl of a stand mixer fitted with a whisk attachment (or use a bowl and a hand mixer), beat the butter, sugar, and vanilla until very fluffy and white.

Add the cream cheese and beat until well incorporated.

If desired, color ⅓ of the cream with green food coloring and place it in a piping bag fitted with a nozzle of your choice.

Place the first cake layer on a plate or cake stand and evenly spread some of the filling over it.

Place the second cake layer on top and spread the same amount of filling. Place the third cake layer on top and apply a thin layer of the remaining cream on the top and sides of the cake as a crumb coat. Refrigerate or freeze the cake for 1 hour or until well chilled, the crumb coating is set, and the cake is not wobbly.

Spread the frosting evenly over the top and sides of the cake.

Decorate with the cream in the piping bag and optionally use matcha powder for dusting.

Chill the cake in the refrigerator for at least 2 hours before serving.