Put the egg whites into the bowl of a stand mixer with the whisk attachment (see note 8 below).
Place the larger amount of granulated sugar (i.e., 150g) into a small saucepan, add the water, and stir to moisten the sugar. Bring the mixture to a simmer over medium-high heat until it reaches 230°F/110°C.
While the sugar heats on the stove, turn the stand mixer to medium and gradually pour in the remaining granulated sugar. Whip the egg whites until they form loose peaks and then turn the mixer to low speed until the sugar is ready.
When the sugar reaches 248°F/120°C,remove the pan from the heat. Turn the stand mixer to medium-low speed and slowly pour the sugar between the side of the bowl and the whisk. Try very hard to avoid pouring the sugar onto the whisk because it will whip the sugar onto the side of the bowl and create hard strings of cooled sugar.
After the sugar has been incorporated, increase the speed to medium-high and whisk for 15 minutes, or until the bottom of the bowl is at room temperature and the whites hold stiff peaks. Warm egg whites will melt the butter and cause it to become the wrong texture.
Reduce the speed to medium and add the butter, a few pieces at a time. If it looks like the mixture is broken (i.e., if the buttercream looks curdled), increase the speed of the mixer to bring it back to the correct consistency. If the consistency of the buttercream is too loose after adding all the butter, place the buttercream in the fridge for a few hours.
The buttercream can be made and refrigerated up to 5 days before you need it. Remove buttercream from the fridge a minimum of 30 minutes before using it to bring it to a piping/spreading consistency.