Separate eggs whites, taking care to ensure that none of the yolks get into the whites. Any amount of yolk will prevent the frosting from coming together properly. Place the eggs whites in a clean, dry stand mixer. Use the whisk attachment and whisk on low speed until the egg whites get foamy. Add the cream of tartar and beat on high until stiff but glossy peaks form.
Prepare the sugar syrup. Add sugar and water to a small saucepan and bring to boil until a candy thermometer reaches the soft ball stage, 238°F.
With the mixer on high, pour the hot syrup in a stream into the egg whites. Continue to beat on high for 3 minutes to allow the egg/sugar mixture to cool a bit. Add softened butter 2 tablespoons at a time until all the butter is added. Beat on high for about 4-5 minutes until it's smooth and fluffy, beat in vanilla (and/or food coloring, if desired) Transfer buttercream to a pastry bag.