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1
Combine whites and salt in a very large bowl.
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2
Stir together water and 1 1/3 cups sugar in a 3- to 4-quart heavy saucepan until sugar is dissolved, then bring to a boil over moderate heat, without stirring, brushing any sugar crystals down side of pan with a pastry brush dipped in water.
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3
When syrup reaches a boil, start beating egg whites with an electric mixer at medium-high speed until frothy, then gradually add remaining 2 tablespoons sugar and beat at medium speed until whites just hold soft peaks.
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4
(Do not beat again until sugar syrup is ready.)
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5
Meanwhile, put thermometer into sugar syrup and continue boiling until syrup registers 238 to 242F.
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6
Immediately remove from heat and, with mixer at high speed, slowly pour hot syrup in a thin stream down side of bowl into whites, beating constantly.
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7
Beat, scraping down side of bowl with a rubber spatula, until meringue is cool to the touch, about 10 minutes in a standing mixer or 15 with a handheld.
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8
(It is important that meringue is properly cooled before proceeding.)
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9
With mixer at medium speed, gradually add butter 1 piece at a time, beating well after each addition until incorporated.
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10
(Buttercream will look soupy after some butter is added if meringue is still warm.
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11
If so, briefly chill bottom of bowl in a large bowl filled with ice water for a few seconds before continuing to beat in remaining butter.)
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12
Continue beating until buttercream is smooth.
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13
(Mixture may look curdled before all of butter is added but will come back together by the time beating is finished.)
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14
Add vanilla and beat 1 minute more.
