Crepes: Place flour, granulated sugar, salt, milk, eggs, vanilla, and butter in a blender. Blend well, about 1 minute, scraping down sides as needed. Refrigerate in blender jar at least 2 hours and up to overnight.

Process batter again in blender briefly to remove lumps. Lightly coat a 10-inch crepe pan or 12-inch nonstick skillet with butter. Heat over medium until just starting to smoke. Remove from heat; pour about 3 tablespoons batter into center. Swirl to cover bottom. Reduce heat to medium-low; return pan to heat. Cook until edges are golden and center is dry, about 40 seconds. Flip crepe. Cook 15 seconds more. Slide crepe onto a parchment-lined baking sheet. Repeat with remaining batter, adding more butter and adjusting heat as needed; stack crepes. Let cool completely.

Assembly: For shingled sides on the cake, use the ring from a 10-inch springform pan. Place 1 crepe, golden-side up, on a flat serving plate. Spread 1/4 cup pastry cream over crepe, leaving 1/2-inch border if using ring. Top with a second crepe. Using 24 crepes total, continue layering crepes and pastry cream, ending with a crepe on top; if using ring, slide it down sides of crepes. Refrigerate cake until firm, at least 1 hour and up to 6 hours.

Just before serving, remove ring from cake, if using. Place parchment strips under perimeter of cake. Whisk together confectioners' sugar and matcha; sift over top of cake.