Sift flour, granulated sugar, salt, and matcha into a bowl.
Whisk in the milk and beaten eggs until smooth, then blend in melted butter. Rest batter 20–30 minutes.
Warm a nonstick skillet over medium heat and lightly oil the surface.
Pour about 1/4 cup batter, swirl thin, and cook until edges lift. Flip and cook 10–20 seconds more.
Transfer crepes to a rack or plate and cool completely. Repeat with remaining batter.
Beat mascarpone, powdered sugar, and vanilla until smooth. Stream in cold cream and whip to medium-stiff peaks. Fold in matcha if using.
Place one crepe on a serving plate. Spread a thin layer of cream over the surface.
Stack and repeat with remaining crepes and cream, finishing with a bare crepe on top.
Chill the cake 1–2 hours to set. Dust with matcha, slice, and serve.