Blend: Add the milk, eggs, flour, vanilla extract, salt, sugar, and melted butter to a blender. Blend on high for about 30 seconds, scraping down the sides, until completely smooth.
Heat the Pan: Heat a 10-inch non-stick skillet over medium heat and lightly grease it with butter or oil.
Pour and Swirl: Pour about ¼ cup of batter into the pan and swirl it quickly so it coats the bottom in a thin, even layer.
Cook and Flip: Cook for 30 to 40 seconds, until lightly golden on the edges, then carefully flip and cook for 20 seconds more.
Cool: Stack the crepes on a plate and let them cool completely.
Make the whipped cream
Whip: Whip the cold heavy cream, vanilla extract, and powdered sugar with an electric hand mixer until stiff peaks form.
Assemble the cake
First Layer: Place one crepe on a serving plate and spread 2 to 3 tablespoons of whipped cream over it in a thin, even layer all the way to the edges.
Stack: Repeat with the remaining crepes and cream, pressing each crepe down gently. Chill the cake for at least 1 hour.
Make the chocolate ganache
Heat: Place the chopped dark chocolate in a bowl. Heat the cream until it just simmers, then pour it over the chocolate.
Stir: Let it sit for 10 minutes, then stir until smooth and silky. Cool for 5 to 10 minutes.
Finish: Pour the ganache over the chilled cake and spread it with an offset spatula. Top with fresh berries and chill until set.
Notes
No Blender:Whisk the flour, sugar, and salt in a bowl, whisk in the eggs and ½ cup of milk to a smooth paste, then slowly whisk in the remaining milk, melted butter, and vanilla. Strain out any lumps.
Rest the Batter: 30 minutes of resting makes the crepes even more tender.
Test Crepe: Use the first crepe to adjust the heat and amount of batter.
Thin Crepes: Use just enough batter to coat the bottom of the pan.
Cool Completely: Warm crepes will melt the whipped cream.
Cold Cream: The heavy cream must be very cold to whip into stiff peaks.
Even Layers: Use 2 to 3 tablespoons of cream per crepe and spread it to the edges.
Cool the Ganache: Let it cool for 5 to 10 minutes so it doesn't melt the cream.
Clean Slices: Use a hot, dry knife and wipe it between cuts.
Make Ahead: Cook the crepes up to 2 days ahead and stack them with parchment between each one.
Storage: Keep covered in the fridge for up to 3 days. Freeze the whole cake or slices for up to 2 months.