Chop butter into 1 inch size pieces and set aside.
Place the egg white powder, water, powdered sugar & cream of tartar into the bowl of your stand mixer, and give it a gentle stir with your spatula to make the sugar damp.
Fit the whisk attachment to your stand mixer and lock the bowl with ingredients in place. Whisk on a high speed (speed 8 on a kitchen aid) until the mixture becomes light and fluffy. This took me about 6 minutes. Stop whisking when the mixture forms a meringue with stiff peaks (see the image in the post above for reference).
Turn the speed of your stand mixer to medium/low (speed 4 on a kitchen aid) and slowly add the butter. Add one piece every 30 seconds or so, allowing each piece of butter to be incorporated into the mixture before adding the next. Then add the salt.
Once all the butter has been incorporated, the mixture may look grainy and curdled. This is OK. Turn the speed of you mixer up to high (speed 8) and whip until the buttercream comes together. This stage took me about 5 minutes.
Once the buttercream has come together, remove the whisk attachment, being careful to scrape as much of the buttercream back into the bowl of your stand mixer. Next fit the paddle attachment to your mixer, add the vanilla extract and beat the buttercream on medium speed (speed 4) until it becomes creamy and smooth (about 4-5 minutes).