Instructions

Adjust oven rack to middle position and heat oven to 350 degrees. Line bottom of 9-inch springform pan with circle of parchment paper.
Melt butter in small saucepan over low heat. Remove from heat and set aside. Sift flour, cocoa, and salt together onto large piece of parchment paper; set aside.
Whisk together eggs and sugar in bowl of standing mixer until combined. Place bowl over pan of barely simmering water, making sure that water does not touch bottom of bowl, and heat egg mixture, whisking constantly, until warm to touch, about 110 degrees on instant-read thermometer. Remove from heat and beat at medium-high speed until eggs are pale, cream-colored, voluminous, and form thick ribbon of tiny billowy bubbles that falls from whisk and rests on top of batter for several seconds when whisk is held about 4 inches above egg mixture (this should take 6 to 8 minutes). Beat in vanilla. Turn off mixer, transfer 1 cup egg mixture to medium bowl, and stir in melted butter until combined; set aside.
Grab both ends of sheet of parchment paper holding flour mixture and, with mixer running at lowest speed, slowly sprinkle flour mixture into batter until just barely incorporated (see illustration below). Add melted butter mixture back to batter in standing mixer bowl and, with mixer still running at lowest speed, fold gently to incorporate, being careful not to deflate batter.
Immediately push batter from bowl into prepared springform pan with rubber spatula, holding bowl close to bottom of pan. Smooth top with offset spatula. Bake until cake is deep golden brown and springs back lightly when pressed with a finger, about 35 minutes. Transfer pan to wire rack and cool completely. When cake is cool, run blade of thin metal spatula around inside circumference of springform pan to loosen cake from sides of pan and remove. Invert cake onto plate or baking sheet, remove pan bottom and parchment paper, and reinvert cake onto rack.