Start with the filling. Pour the milk into a small saucepan, and sprinkle over the cornstarch, whisk until combined.
Next, add the honey and sugar stirring continuously over a low heat. When the milk mixture almost starts to boil it will thicken and get a bit lumpy, don't panic! Just keep stirring until it smooths out. Continue to stir the now thick milk mixture over the heat for an additional 1-2 minutes, to cook out the cornstarch flavor.
Take off the heat and pour into a bowl or shallow dish. Cover the mixture with cling wrap, pushing it all the way to the top of the custard to prevent a film from forming and chill this in the refrigerator until cold.
Next, make the cake by combining the sugar, honey, matcha powder, and eggs in a large bowl. Mix until it almost triples in size, is lighter in color, and becomes thick and fluffy. This will take about 7-10 minutes. If you dribble some of the batter on itself it should hold a "ribbon" shape for 4-5 seconds.
Once the batter has reached the correct consistency sift over the cake flour, and gently fold the flour in until all combined.
Heat your oven to 350˚F (175˚C) and butter your baking sheet. Place a piece of parchment paper (a few inches larger than your baking sheet) onto your baking sheet. Using a rubber scraper (or your hand) push out any bubbles.
Pour the batter into the prepared baking sheet and bake for 8-10 minutes.
NOTE: You'll know it's done when the cake is slightly risen, turning just a bit golden, and you can smell it. Also, if you gently press your fingertips on the surface of the cake, and no indentations are left, it's done.
In a clean bowl, whip the heavy cream with electric beaters until it is thick and pretty stiff, little peaks should form when you lift the beaters.
Grab your chilled custard from the fridge. Add one tsp of vanilla extract. Take the same beaters and whisk your custard, it will look funny at first, but after a few moments it will become nice and smooth.
Fold the whipped cream into the custard until they are combined.
Cool your cake for 2-3 minutes on the baking sheet. Lay a fresh sheet of parchment beside your cake and sprinkle it with powdered sugar.
Lift the cake with the sides of the parchment onto your table. Flip the cake onto the sugared parchment paper.
Remove parchment paper from the flipped cake.
Slather the filling onto your cake.
Roll it up, using the parchment to help.
Wrap the whole thing in cling wrap and chill for two hours before slicing.
Slice into pieces of your desired thickness and serve.