Fill a medium pot with a few inches of water and bring to a simmer.
In the bowl of a stand mixer, combine the egg, sugar, and water. Place the bowl over the pot of simmering water and whisk until sugar is dissolved and mixture reaches at least 165 F, about 5 minutes. Remove from heat.
Place in mixer with whisk attachment and whip on high for about 7-9 minutes, until pale in color and bowl is cool to the touch. Allow to cool completely.
With the mixer on medium, add in the butter, 1 tablespoon at a time until fully incorporated and texture is light and fluffy.