This filling was used to assemble layers of crepes for the Green Tea Crepe Cake. Martha made this recipe on episode 508 of Martha Bakes.
In a medium saucepan, combine milk, 1/4 cup sugar, vanilla bean and seeds, and salt. Cook over medium until mixture comes to a simmer. Add matcha; whisk to combine.
In a medium bowl, whisk together egg yolks, cornstarch, and remaining 1/4 cup sugar. Whisking constantly, slowly pour about 1/2 cup hot-milk mixture into egg-yolk mixture. Continue adding milk mixture, 1/2 cup at a time, until incorporated. Pour mixture back into saucepan and cook over medium, whisking constantly, until it thickens and comes to a boil. Let boil, still whisking, 2 minutes.
Remove from heat and strain through a fine sieve into a bowl. Add butter and stir until butter melts and mixture cools, about 5 minutes.
Cover with plastic wrap, pressing it directly onto surface of pastry cream to prevent skin from forming. Refrigerate until chilled, at least 2 hours and up to 2 days.
Just before using, stir pastry cream with a flexible spatula until smooth. Whip heavy cream to soft peaks and fold into pastry cream.