In a stand mixer bowl, cream the butter with the flat beater on medium-high speed for about 2 minutes, until smooth and creamy. Scrape the butter into another bowl and set aside for later. Wash the mixer bowl well.
In the degreased mixer bowl, whip together the egg whites and cream of tartar, just until foamy.
In a small saucepan, stir 150 g of the sugar, the orange zest, and the water together. Heat on medium heat, stirring, until the sugar dissolves. Keep on low heat.
While the syrup comes up to temp, use the whisk attachment on the mixer to start beating the eggs, increasing the speed to medium-high. When soft peaks have formed, add the remaining 50 g sugar and beat until stiff peaks form.
Bring the syrup to a boil and cook, checking the temperature frequently with your Thermapen ONE until the temperature reaches 248-250°F (120°C), adjusted 1°F less for every 500 ft above sea level you're cooking at.
Turn the mixer to low speed and slowly pour the syrup into the bowl, right by the edge. Increase the mixer speed to high and beat for a few seconds, then turn the speed down to medium and beat for 2-4 minutes, letting the heat escape, until the meringue reaches 70°F (21°C)—use your Thermapen to check it periodically.
Scrape the butter into the meringue mixture and beat on medium speed until the icing is smooth and creamy. The butter may look curdled, but keep going. The temperature should be between 68 and 70°F (20 and 21°C).
Beat in the vanilla and the melted chocolate until the mixture is homogenous with no chocolate streaks. Scrape down the bowl and mix for one more minute.