Beat the butter until smooth and set aside. In a small saucepan, combine the water and 3/4 cup of sugar. Stir until the sugar is dissolved. Slowly heat the mixture, stirring constantly, until it starts to bubble. Reduce heat to low and insert a candy thermometer. Do not contiue to stir.
In a large bowl of an electric mixer, beat the egg whites at medium speed until foamy. Add cream of tartar and beat at high speed until soft peaks form. Gradually add the remianing 1/4 cup sugar and beat until stiff peaks form.
Meanwhile, boil th esuagr mixture until it reaches 248 to 250 degrees F. on the candy thermometer. Do not let the temperature go above 250 degrees F. Turn off the heat and immediately pour the mixture into a glass measuring cup to stop the sugar from cooking. Pour a little of the sugar mixture onto the egg whites and beat them on low. Slowly add the rest of the sugar and then beat on high for 2 minutes. Beat on low until the mixture is cool. Add the butter, 1 tablespoon at a time, to the egg white mixture, beating continuously on low until all the butter is added. If the mixture starts to separate, beat on high for a few seconds until it solidifies. Beat until smooth, then add the flavoring. This icing can be stored at room temperature for 2 days or refrigerated for 10 days.