In a large bowl, whisk together flour, matcha powder, sugar, and salt.
Gradually whisk in milk and eggs until smooth. Stir in melted butter.
Heat a lightly oiled griddle or non-stick frying pan over medium heat. Pour 0.25 cup of batter onto the hot griddle. Tilt the pan with a circular motion so that the batter thinly coats the surface.
Cook the crepe for about 2 minutes, until the bottom is lightly browned. Loosen with a spatula, flip, and cook for another minute. Repeat with remaining batter.
In a large bowl, whip heavy cream with powdered sugar and vanilla extract until stiff peaks form.
Place one crepe on a serving plate and spread with a thin layer of whipped cream. Repeat with remaining crepes and cream, stacking them on top of each other.
Refrigerate the crepe cake for at least 30 minutes before serving. Dust with matcha powder before serving.
Notes
For a richer flavor, add a tablespoon of rum or other liquor to the crepe batter. Garnish with fresh berries or a dusting of powdered sugar.