Preheat the oven to 170℃ (150℃ fan/340℉). Lightly grease a 25 x 38 cm (10 x 15 in) baking sheet and line the bottom with parchment paper.
Add the flour and salt to a bowl. Sift in the matcha powder and whisk to combine. Set aside.
Place egg whites in a large mixing bowl, or the bowl of a stand mixer. Be very careful not to get any egg yolk or oil in the bowl. Using an electric mixer or a stand mixer fitted with the whisk attachment, beat on medium speed until frothy. With the mixer still running, gradually pour in half of the granulated sugar. Continue beating until stiff peaks form. Set aside.
In another mixing bowl, combine the egg yolks with the other half of the granulated sugar, the vegetable oil, milk, and vanilla extract. Beat until smooth (about 1 minute). Add the dry ingredients and beat until just combined.
Using a rubber spatula, gently fold in about ⅓ of the whipped egg whites, taking care not to deflate the mixture. Add the remaining egg whites, and keep folding until you can't see any more streaks. Scrape the sides and bottom of the bowl to ensure everything is well incorporated.
Pour the cake batter onto the prepared baking sheet. Smooth it out as evenly as possible, then tap the pan on the counter a couple of times to release any large air pockets. Bake for 10-12 minutes or until the cake springs back when pressed and a toothpick inserted into the centre comes out clean.
Remove from the oven and immediately cover with a clean tea towel or a piece of aluminium foil. Leave to steam for about 10 minutes. Remove the tea towel or foil and run a knife along the edges of the sponge. Dust the surface of the cake with powdered sugar, then carefully flip the cake out onto a tea towel or a piece of parchment paper. Peel off the parchment paper, then leave on the countertop to cool for 15-20 minutes.
Flip the cake over again so that the browned side is facing up. Starting from the short end, carefully roll the cake up in the parchment paper or tea towel. Set aside while you prepare the filling.