Yes to everything Matthew and Charles said. Genoise has to be syruped or it will be dry, and a little lacking in flavor (though Rose’s are more flavorful than most).
For Genoise, definitely take the butter solids to a rusty-brown color, buerre noisette.
It should be taller than 1”. There are several things that can affect the height:
-If your mixer is less powerful than a Kitchen Aid (like a hand mixer), you will need to beat the eggs on high for at least ten minutes (at least five minutes for a Kitchen Aid or similar).
-The full amount of beaten eggs specified in the recipe (for a four-egg genoise, this is a scant cup) needs to be folded into the browned butter or it will be too heavy.
-The cake flour/cornstarch (or Wondra) must be sifted over the eggs in two batches.
-Use a balloon whisk or slotted spoon for folding.
-Don’t fold more than necessary.
Overbaking- if you watch the genoise towards the end of baking, the center will peak and then very slightly shrink/flatten. It will also shrink a little from the sides, unless you are using cake strips. As soon as that little bit of shrinking happens, it is done.