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Sift the flour through a sieve, mix with baking powder and salt. Put aside.
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Whisk the room temperature butter with the sugar, vanilla sugar until fluffy. Add one of the eggs, mix it very well and just then add another one. Mix it until smooth.
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Divide flour into four parts and the milk into three parts. Add the first part of the flour, mix it well, then pour the first part of milk, mix well again. Repeat with the rest of the flour and milk (flour, milk, flour, milk, flour, milk, flour). Stir until smooth, but do not overmix.
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Line a 20 cm diameter round pan with baking paper (preferably only the bottom, you can grease the sides with butter), pour one-third of the dough, and beat several times on the table to let the air out. Divide the remaining dough into two more pieces and pour it into the other two pans (or wait for the first one to bake, then bake another one).
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Bake for about 45 min. in an oven preheated to 175-180 degrees Celsium. Remove the baked vanilla cake from the oven and leave to cool completely (preferably overnight). The cooled cake can be trimmed and spread.