Combine all liquid ingredients in a blender. Add dry ingredients and melted butter; mix on high. Strain batter. Let rest for at least 30 minutes.

Heat a nonstick 10-inch skillet over medium-high heat. Brush bottom and sides of pan with melted butter. Ladle 1 ice-cream scoopful of batter into skillet and swirl to coat bottom evenly. Cook until bottom is lightly browned, about a minute. Using a spatula or your fingers, flip crepe and cook until other side is lightly browned, about 20 to 30 seconds.

Transfer crepe to a platter. Layer crepes on top of each other. Don’t worry if crepes are crispy at first, they will soften after letting them sit.

To make green tea pastry cream:

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.

To assemble:

Cut out cake circles if you want to neaten the edges. Lay first crepe on the serving plate and spread with 1/4 cup pastry cream. Repeat with all the crepes until you place the last crepe.

Chill the cake in fridge. Sprinkle with matcha powder before serving.