Yield: 9-inch cake
Brown the butter. In a small pan, cook the butter until it is fragrant and the milk solids have turn brown. Set aside.
In another pan, boil the milk. Turn off heat and allow to cool for 10 minutes.
Beat together eggs, flour, sugar, and salt in a stand mixer with a paddle attachment. Slowly add the hot milk and browned butter. Mix until smooth and combined. Pour into an airtight container and refrigerator overnight (or at least 2 hours).
In a saucepan, bring milk and vanilla bean (along with scrapings) to a boil. Set aside and let vanilla steep for 10 minutes, then remove the bean. Prepare an ice bath, buy filling a large bowl with ice. Have a smaller bowl ready (bowl large enough to hold the finished pastry pastry).
In another pot, whisk together yolks, sugar, and cornstarch. Temper in hot milk by gradually whisking it in. Place the pot over high heat and bring to a bowl, whisking vigorously for a minute or two.
Press the pastry cream through a fine-meshed sieve into the small bowl and place over the ice bath. Stir the pastry cream until the temperature reaches 140 degrees F. Stir in the butter. When the pastry cream is cool, cover and refrigerate.
Bring the crepe batter to room temperature. Place crepe pan over medium heat. Lightly grease the surface with oil and add about 3 Tbsp of batter (if using a 9 inch pan) and tilt pan in a circular motion to cover the surface of the pan.
Cook until the bottom just begins to brown and then flip the crepe with your fingers. An offset spatula is helpful if your fingers cannot withstand the heat. Cook on the other side for no more than 5 seconds. Flip the crepe into a parchment lined baking sheet. Repeat until you have used all the batter or have at least 20 prefect crepes.
Whip the heavy cream with the tablespoon of sugar and Kirsch. Whip to soft peaks. Fold into the pastry cream in three stages.
Lay 1 crepe on a cake plate. Spread a thin later of pastry cream over the crepe. Cover with another crepe and repeat to make a stack. Remember to save your best looking crepe to place on top.
Chill cake for at least 2 hours. Let cake sit at room temperature 30 minutes before serving.
Optional: Before serving, sprinkle the top with 2 tablespoons of sugar and caramelize with torch.