In the bowl of a standing mixer with a whisk attachment, add eggs, and cream of tartar. Mix on medium until frothy and then slowly add ¼ cup of sugar.
Turn to medium high and mix until soft peaks form.
While whipping the egg whites, start heating the sugar syrup. You want them both done about the same time, so if the egg whites reach soft peaks prior to the sugar syrup reaching the right temperature, turn the speed to the lowest setting and continue mix until the syrup is done.
To make the sugar syrup, add the remaining 3/4 cup of sugar and water to a medium saucepan. Stir to combine.
Cook a few minutes over low heat until the sugar is dissolved the sugar syrup looks clear.
Once the sugar dissolved, turn the heat up to medium high and heat the sugar syrup without stirring until it reaches 235-240 ℉.
Once it hits the right temperature immediately remove from heat.
While mixing the egg whites on low, very slowly and carefully pour in the hot sugar syrup.
Once you’ve added all the sugar syrup to the egg whites, turn up the speed to medium to medium high and continue whipping the egg whites until they cool down completely and no longer warm to the touch, about 10-15 minutes.
Once the egg whites have cooled, starting adding the softened butter one tablespoon a time, making sure each piece is combined before adding the next.
Also, switching to the paddle attachment at this time can help keep the buttercream from breaking or curdling, but is not necessary.
Continue mixing until the buttercream comes together to a silky smooth frosting. If the frosting starts to turn liquid or soupy, put in the fridge for 15 minutes to firm up, then continue mixing. See troubleshooting for more info.
Once the buttercream comes together to form a smooth frosting, add the vanilla and salt and mix until combined. Then the frosting is ready to use on your favorite cakes and desserts.