In a small saucepan, combine the 1 ½ cup of granulated sugar with the water.
Place over high heat and cook to soft-ball stage (235-240 degrees F) Read more in-depth about this below. Do not stir.
While the sugar cooks, fit a stand mixer with the whisk attachment. Pour egg whites in the bowl and whip on medium until the eggs get frothy. Slowly add the ⅜ cup of sugar to the egg whites.
Turn the mixer to high and whip until stiff peaks form. If the meringue is done before the sugar, turn it down to the lowest speed.
When the sugar is ready keep the mixer on the lowest speed and very carefully and slowly pour the sugar down the side of the bowl into the meringue.
When all of the sugar is added turn the mixer to high and mix until the outside of the bowl has cooled down and is warm.
Start to add the cubes of butter slowly, about 1 every ten seconds, while continuing to whip the buttercream.
Add the vanilla and continue to whip on high for about 10 minutes or until it is the desired consistency.
You can add food coloring or other flavorings at this point.