Place egg whites and salt in a large bowl.
In a 3.5-qt sauce pan, stir 1 1/3 c. sugar and 2/3 c. water together. Make sure the sugar has completely dissolved. Heat this liquid over medium-high heat, bringing it to a boil.
While the sugar syrup comes to a boil, beat the egg whites and salt with an electric mixer at medium-high speed, until the eggs are frothy. Lower mixer speed to medium and gradually add the 2 Tbsp. of sugar. Beat until you have soft peaks, then stop.
Measure the temperature of the sugar syrup with a candy thermometer. The syrup should register 238ºF - 242ºF.
Remove syrup from the heat. Gradually add the syrup to the egg whites in a thin stream down the side of the bowl. As you add the syrup, combine the syrup and egg whites with an electric mixer on high speed. While beating the egg white mixture, scrape down the sides of the bowl occasionally. Do this until the egg mixture (meringue) is cool to the touch. This might take 10 - 15 minutes.
When the meringue has cooled completely, gradually add the softened cubes of butter. Completely incorporate each addition of butter before adding more. The frosting will go through various stages before it reaches a smooth, creamy consistency.
When you reach a creamy consistency, add the vanilla, lime juice and zest and mix for an additional minute. Your fresh Lime Butter Cream is now ready to serve, to spread and to top off with shredded coconut.
Spread generous amounts of this Lime Butter Cream on our delectable Coconut Lime Cupcakes, then gently press coconut into it.
Recipe was created especially for the Calphalon 3.5-qt. Sauce Pan.