Preheat oven to 350.
Line bottom of 9-inch springform cake pan with parchment paper.
Melt butter in saucepan over medium heat.
Remove from heat.
Transfer butter into a small metal bowl.
Lightly whisk in vanilla; set aside.
In a medium mixing bowl, whisk together flour and cocoa powder; whisk until combined.
In a separate large bowl, whisk eggs and sugar until blended.
Pour water in a large skillet and bring to a simmer.
Place bowl with egg mixture in the skillet, whisking constantly until egg mixture is lukewarm, about 2 minutes.
Remove bowl from water.
Place the bowl with butter in same skillet over low heat to keep warm.
Using electric mixer, beat egg mixture until cool and tripled in volume, about 5 minutes.
Sift 1/3 of flour-cocoa mixture over egg mixture and gently fold in with rubber spatula.
Fold in remaining flour-cocoa mixture in 2 more additions.
Fold 1 cup of cake batter into the warm butter; fold until incorporated.
Using rubber spatula, gently fold butter-cake batter mixture into remaining cake batter.
Transfer the batter to previously prepared pan.
Bake for 30 minutes, or until a toothpick inserted into center of cake comes out clean and the top of cake springs back slightly when gently pressed.
Cool completely in pan on rack.
Remove completely cooled cake from pan and invert cake onto rack; remove parchment and set cake aside.