In a blender, combine the 4 eggs, 2 cups whole milk, 1 cup flour, 1/4 cup sugar, 1/4 teaspoon salt, 6 tablespoons melted butter, and 1 teaspoon vanilla extract. Blend on high for 30 seconds, until the batter is completely smooth with no flour flecks and runs off a spoon like heavy cream.

Pour the batter into a bowl, cover, and refrigerate for at least 30 minutes and up to 2 days. This rest lets the flour fully absorb the liquid so the cooked crepes turn out tender instead of rubbery.

Heat a 9 inch nonstick skillet over medium heat and brush it with a little melted butter. Pour in a scant 1/4 cup of batter, immediately lifting and tilting the pan so the batter spreads into one thin, even circle.

Cook the crepe for about 45 seconds, until the surface turns matte and the edges lift away from the pan without sticking. Flip it with a thin spatula and cook the second side for 15 to 20 seconds, just until set, then slide it onto a plate.

Repeat the pouring and cooking with the remaining batter, re-buttering the skillet every 3 or 4 crepes and stacking the finished ones on the plate. You need about 20 crepes for real height in the cake, so a few extra are useful insurance against a torn one.

Spread the stacked crepes loosely or drape a clean towel over them and let them cool completely at room temperature, about 20 minutes. Warm crepes will melt the whipped cream the moment you start layering, so do not skip this.

In a chilled bowl, beat the 2 cups cold heavy cream, 1/3 cup confectioners' sugar, and 1 1/2 teaspoons vanilla extract with a hand mixer on medium high speed until the cream holds a soft peak that curls over when you lift the beaters, 2 to 3 minutes. Stop as soon as you see that curl, before the cream looks grainy.

Pat the 1 1/2 pounds of sliced strawberries dry between layers of paper towel. Wet strawberries bleed juice into the cream and turn the layers pink and soggy by the time the cake chills.

Set one crepe on a cake stand or flat plate and spread about 2 tablespoons of whipped cream over it in a thin, even layer, stopping 1/2 inch from the edge. Scatter a single layer of sliced strawberries over the cream.

Top with another crepe and repeat the thin layer of cream and strawberries, continuing until all 20 crepes are used, finishing with a plain crepe on top with no filling. Press down gently every 4 or 5 layers to keep the stack centered and level as it grows.

Spread a thin cap of the remaining whipped cream over the top crepe and arrange the 8 to 10 whole strawberries over the surface, trimming the stem ends flat so they sit level. Cover loosely and refrigerate for at least 2 hours, until the side of the cake feels firm rather than springy when you press it.

Slide a thin, sharp knife straight down through the chilled cake in one motion, wiping the blade clean between cuts. Lift each wedge onto a plate so the striped layers show on their side, and serve cold.