Preheat oven to 350 degrees. Line bottom of jelly-roll pan with parchment paper. Combine clarified butter and vanilla in small bowl. Keep hot until needed or reheat for a few seconds just before using--this is important! Combine flour with 3 tablespoons of the sugar. Sift together twice; return to sifter and set aside.
In a large heatproof mixing bowl, use a whisk to combine eggs and sugar. Place bowl in or over a saucepan containing 1 to 2 inches of barely simmering water. Heat eggs to lukewarm, (check by touching), whisking occasionally. Remove bowl from heat. Beat egg mixture at high speed with an electric mixer until it has cooled, tripled in bulk, and resembles softly whipped cream. Sift about 1/3 of the flour mixture over the whipped eggs. Use your largest rubber spatula to fold the mixture, by hand, quickly but gently until combined. Sift and fold in half the remaining flour mixture; sift and fold in the rest. Scoop about 1 cup of the batter into another bowl and fold it together with the hot clarified butter and vanilla. When completely combined, fold the butter mixture back into the remaining batter. Turn batter into prepared pan, and spread evenly over pan. Bake 15 to 20 minutes or until cake shrinks slightly from the edges of the pan and top springs back when pressed with fingers. Run a small knife around the edges of the cake to release it from pan. Invert pan onto a sheet of foil and remove pan. Cool cake without removing parchment pan liner (cake will steam slightly between the parchment and the foil, making it flexible enough to roll without cracking later).
Recipe courtesy of Alice Medrich