MAKE THE VANILLA SAUCE
In a saucepan, combine the milk, cream, and vanilla bean paste. Warm over medium-low heat until steaming and just beginning to simmer, about 3–4 minutes. Do not boil.
While the milk mixture warms, in a separate bowl whisk together the egg yolks, sugar, cornstarch, and salt until lighter in color and the sugar is fully dissolved, about 1–2 minutes.
Slowly drizzle the warm milk mixture into the egg yolk mixture while whisking constantly to temper the eggs.
Pour the mixture back into the saucepan.
Cook over medium-low heat, stirring constantly, until the sauce thickens enough to coat the back of a spoon, about 3–5 minutes.
Remove from heat and keep warm, stirring occasionally, while you make the pancakes.
MAKE THE KAISERSCHMARRN
In a large bowl, whisk the egg yolks with 2 tablespoons of the sugar until pale and slightly thickened, about 1–2 minutes. Whisk in the milk and vanilla extract.
Add the flour and salt directly into the wet mixture and whisk just until smooth and lump-free.
In a clean bowl, whip the egg whites using a stand mixer fitted with the whisk attachment or a hand mixer on medium speed until foamy. Increase to medium-high speed, gradually add the remaining 2 tablespoons of sugar, and continue whipping until stiff, glossy peaks form, about 2–3 minutes.
Fold a small scoop of the whipped egg whites into the batter to loosen it. Pour the batter into the remaining egg whites and gently fold until just combined, keeping the mixture light and airy.
Heat a large frying pan/skillet over medium-low heat and melt 1 tablespoon of the clarified butter. Pour in the batter and spread gently.
Let the pancake cook undisturbed for 3–4 minutes, until the bottom is golden and the top is mostly set.
Using a spatula, cut the pancake by making long cuts vertically and horizontally to form rough squares or rectangles. It will get messy — don’t worry about making it perfect. I like using a metal spatula to cut and a flexible rubber spatula to help flip.
Flip sections as needed and cook for another 2–3 minutes, until cooked through but still soft.
Tear the pancake into rustic pieces. Push the pieces outward to create an empty space in the center of the pan.
Add the remaining butter and sugar to the center. Let the sugar dissolve into the butter for 30–45 seconds, then toss everything together to coat and caramelize the pieces, about 1–2 minutes.
Remove from heat and dust generously with powdered sugar.