Genoise Cake

PREHEAT THE OVEN Twenty minutes or longer before baking, set an oven rack in the lower third of the oven. Set the oven at 350F/175C.
Have ready by the cooktop a 1 cup/237 ml glass measure with a spout, with a fine-mesh strainer suspended over it.

PREPARE THE PAN Grease and flour the sides, grease and paper the bottom

CLARIFY AND BROWN THE BUTTER Cut the butter into tablespoon-size pieces and set it in a small saucepan. On very low heat, melt the butter, stirring often with a silicone spatula. Raise the heat to medium and boil, stirring constantly to prevent sputtering. As the water evaporates and the bubbling becomes quieter, it's fine to raise the heat if you continue to stir constantly, until the milk solids on the spatula become a deep brown. (Take the pan off the heat briefly so that the bubbles become less rapid and you can check the progress and prevent burning.)
Immediately pour the butter into the strainer. Weigh or measure the butter into a 2 cup/500 ml glass measure with a spout. Add the vanilla and set it in a warm place. The clarified butter should be almost hot (110° to 120°F/43° to 49°C) when added to the batter.

MIX THE FLOURS In a medium bowl, whisk together the flour and tapioca flour. Sift the mixture onto a piece of parchment.

SEPARATE AND MEASURE THE EGGS In the bowl of a stand mixer, using a long-handled wire whisk, lightly combine the measured egg yolks and egg whites. Lightly whisk in the sugar.

MAKE THE BATTER Set the mixer bowl over a saucepan of simmering water. Stir constantly with a long-handled wire whisk only until warm to the touch-about 4 minutes. An instant-read thermometer should read 105° to 110°F/41° to 43°C.
Set the bowl in the stand and attach the whisk beater. Beat the mixture on high speed for a full 5 minutes but not longer. It will more than quadruple in volume and become very thick and airy. (In a 5 quart/4.7 liter mixer bowl, it will come to about two-thirds high.)
Remove about 60 grams/1 cup of the mixture and thoroughly whisk it into the butter.
Sift half of the flour mixture over the remaining egg mixture and fold it in gently but rapidly with a flat wire whisk, slotted skimmer, or silicone spatula, until almost all the dry particles have disappeared. Repeat with the remaining flour mixture until the dry particles have disappeared completely. Fold in the butter mixture until just incorporated. Use a silicone spatula to reach to the bottom of the bowl to ensure that it is evenly mixed.
Pour the batter into the prepared pan and, if needed, smooth the surface evenly with a small offset spatula. The pan will be about two-thirds full.

BAKE THE CAKE Bake for 20 to 30 minutes, or until golden brown. It will rise to the top of the pan and lower slightly shortly before it is fully baked. The cake is done when it starts to shrink slightly from the sides of the pan and springs back when pressed lightly in the center. Avoid opening the oven door before the minimum time or the cake could fall.

UNMOLD AND COOL THE CAKE To prevent collapse of the delicate foam structure, the genoise must be unmolded as soon as it is baked
Set the cake pan on one of the coated wire racks. Run a small metal spatula between the sides of the pan and the cake, pressing firmly against the pan. Immediately invert it onto the other wire rack, leaving the parchment in place. Immediately reinvert onto the first wire rack. The firm upper crust prevents sinking and results in a light texture. Cool completely.

MAKE THE SYRUP In a small saucepan with a tight-fitting lid, bring the sugar and water to a rolling boil, stirring constantly. Cover immediately, remove it from the heat, and cool. Transfer to a 1 cup/237 ml glass measure with a spout and stir in the liqueur or vanilla. If necessary, add enough water to equal 200 grams/¾ cup/177 ml.
The syrup can be stored for 1 month refrigerated in an airtight container.

COMPOSE THE CAKE Use a long serrated knife and your fingertips to remove the top crust, which would interfere with syruping. Invert the cake onto a wire rack. Remove the parchment and scrape off any remaining bottom crust to help the syrup penetrate.
Use a pastry brush to dab half the syrup evenly onto the bottom of the cake. It is now more tender and fragile. Carefully invert it onto a plastic-wrapped cardboard round or a serving plate and apply the remaining syrup to the top of the cake.
Cover the cake with plastic wrap until ready to frost.