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In a medium saucepan, combine the sugar and water. Bring to a boil over medium heat, swirling occasionally to encourage the sugar to dissolve, about 5 minutes. Reduce the heat to medium-low and let the sugar mixture continue to boil gently, without stirring, while you prepare the egg yolks.
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In the bowl of a stand mixer fitted with the whisk, beat the egg yolks on medium-high speed until thick and pale yellow in color, about 5 minutes, pausing halfway to scrape the bowl.
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Add the salt and whisk on medium speed to distribute, another 30 seconds.
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Use a digital thermometer to test the temperature of the sugar mixture; once it's between 240°F and 250°F, remove it from the heat.
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With the mixer running on medium speed, carefully and slowly start to pour the sugar mixture down the side of the mixing bowl (avoid pouring it directly onto the whisk) — once about half the sugar mixture has been added, you can increase the stream slightly and pour a bit faster.
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Once all the sugar mixture has been added, increase the mixer speed to high and whisk until the mixture is pale, fluffy, and cooled to 80°F to 90°F, about 5 minutes.
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Reduce the mixer speed to medium and add the butter 1 to 2 tablespoons at a time, allowing each addition to incorporate fully before adding the next.
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Once all the butter has been added, stop the mixer, scrape the bowl, and add the vanilla. Whisk on medium speed to distribute, another 30 seconds. The mixture should be thick, creamy, shiny, and pale yellow at this stage.
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Use the French buttercream as desired, to fill macarons, frost cake or cupcakes, etc.
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Store any leftover French buttercream in the refrigerator for up to 1 week or in the freezer for longer storage. Bring refrigerated or frozen buttercream to room temperature before using. If needed, rewhip until smooth and pipeable.
