1. Preheat oven to 350 degrees with a rack in center. Butter a 12-by-17-inch jelly-roll pan or rimmed baking sheet. Line with parchment paper; butter and flour parchment. Set aside.

2. Combine sugar, eggs, and salt in a heat-proof mixing bowl set over a pan of simmering water. Whisk until sugar is dissolved and mixture is warm to the touch, 1 1/2 to 2 minutes.

3. Attach bowl to mixer; using whisk attachment, beat on high speed until mixture is very thick and pale, 6 to 8 minutes. Gently transfer to a large, wide bowl. Combine butter and vanilla in small bowl. Sift flour over sugar mixture in three batches, folding gently after each; add butter mixture in steady stream with the third. Pour into pan; smooth with an offset spatula.

4. Bake until cake is lightly golden brown and springy to the touch, 10 to 12 minutes. Transfer to a wire rack to cool completely.