Place all crepe ingredients in a blender and mix on low speed until incorporated. Stop the blender once or twice to scrape down the sides and to make sure there are no flour pockets. Crepe batter should have the consistency of heavy cream.
Let the batter stand at room temperature for 15 minutes, or cover and refrigerate no longer than overnight. Stir the batter before using.
Heat a 9-1/2-inch nonstick skillet or crepe pan on the stove over medium heat and lightly brush with vegetable oil or melted butter. Pour 1/4 cup batter into the skillet and swirl the pan until the batter covers the bottom. Crepes will be very thin (about 1/16-inch).
Cook until lightly browned, about 2-3 minutes. Loosen edges and flip with a thin spatula or crepe turner. Cook on the second side until light golden marks appear.
Remove crepe from pan and repeat with remaining batter, greasing the pan as needed. (Makes about 20 crepes.)
Make the Diplomat Cream
Combine half and half, 1/3 cup sugar, and salt in a heavy-bottomed saucepan. Heat until bubbles form around the edges and wisps of steam rise from the pot. Remove from heat.
While half and half mixture is heating, whisk together egg yolks, remaining 1/3 cup sugar, and cornstarch in a bowl until combined and a light yellow color.
Temper the egg mixture by slowly pouring in about half of the heated liquid, whisking constantly. Whisk tempered egg mixture back into the remaining liquid. Cook over medium-low heat, whisking constantly, until thick and smooth.
Remove from heat and pass pastry cream through a mesh strainer into a bowl. Discard any small egg solids in the strainer.
Whisk in vanilla bean paste, rosewater, and butter until smooth. Cover pastry cream with a piece of plastic wrap pressed directly onto the surface to prevent a skin from forming. Refrigerate until well chilled.
When ready to assemble the crepe cake, whip 1-1/2 cups heavy cream until peaks form. Stir about 1/3 of the whipped cream into the chilled pastry cream to lighten it. Gently fold in the remaining whipped cream.
Assemble and Serve
Place 1 crepe on a cake plate or stand. Spread with 1/3 cup Diplomat cream, leaving about a 1/2-inch border. Continue layering crepes and Diplomat cream until all are used, ending with a crepe.
Cover with plastic wrap and chill for 2 hours.
Whip 1/2 cup cream with granulated sugar and extracts until peaks form. Top crepe cake with whipped cream and decorate with raspberries, and edible rose petals (if using). Sprinkle with chopped pistachios. Slice into wedges and serve.
To garnish with sugar-frosted rose petals:
Rinse about 24 edible rose petals and gently pat dry. Beat an egg white with a few drops of water. (Use pasteurized egg whites if raw egg consumption is of concern.) Use a pastry brush to apply the egg wash to each rose petal. Sprinkle with superfine sugar on both sides. Dry rose petals in a single layer for at least 2 hours.