Generously butter and sugar the springform pan
Slice the butter into the bowl of the stand mixer. Add the sugars and beat until the mixture is very lightl and fluffy, about 3 minutes. Add the egg yolks and vanilla and mix until well blended.
Sift the flour and baking powder into the bowl and beat on low until just blended. Remove the bowl, scrape down the sides, mix once quickly with a spoon, and then scrape everything into the pan. The dough will be sticky.
Spread the dough into the pan, smoothing the top with the back of a wet spoon or your fingers. Pour half of the egg wash onto the dough and use your fingers to smooth out the top. Pour out any excess egg wash from the cake and discard any remaining wash.
Using a wet fork, press in gently and drag the fork across the surface to make a cross then add in additional fork strokes across the surface in a decorative pattern. Place in the refrigerator for 45 minutes.
After 30 minutes begin preheating the oven to 325 degrees F.
After the dough has chilled for 45 minutes, bake it in the oven for 45 minutes. Do not remove it from the oven or turn off the heat as the cake will be going back in.
Lacquer
With a fork, beat together the ingredients for the lacquer. Brush the top of the cake with this mixture (it might deflate a little so work quickly) then continue to bake for another 10 minutes, until it has a slightly shiny top and a tester comes out clean.
Leave the cake to cool in the pan for 15 minutes before you unmold it.