To prepare Génoise,
Line a 9 x 13 baking pan with parchment paper.
Sift flour with a sieve or a fine mesh strainer.
Combine sugar, eggs and vanilla in a mixer. Run mixer until the batter forms ribbons.
Add half the flour into the batter and fold carefully until well incorporated. Add rest of the flour and combine well.
Pour into baking pan.
Bake at 320°F for 15-20 minutes or until golden brown. Remove from oven let cool.
To prepare Syrup,
Put all ingredients in a pot over medium heat until it boils. Set aside and let cool..
To prepare Buttercream,
Cut the butter into small squares.
Heat sugar and water in a pan until 250° F.
Put egg yolks in mixer and mix at medium speed.
Once the sugar/water mixture is at 250° F, pour into the mixer with the yolks and mix at high speed until cooled.
Add the butter. Mix until well incorporated
Add vanilla extract and rum.
To assemble vanilla cake with frosting,
Cut the cake in half horizontally.
Coat both sides with the syrup.
Spread one layer of cream on the bottom half..
Stack other half on top.
Carve the edges off of the cake.
Spread icing over the top and sides of the cake.
You can use a piping bag for creative application of icing.
Cut into slices and serve.