In the bowl of a stand mixer, place egg whites, with cream of tartar and 1/4 cup sugar nearby.
Heat 3/4 cup sugar and 1/4 cup water in a small saucepan. Heat over medium high heat until sugar is dissolved. When sugar reaches 230F on a candy thermometer, turn mixer on medium high. When egg whites are frothy, add cream of tartar. Gradually add the 1/4 cup sugar.
When egg whites begin to form soft peaks, turn the mixer down to medium low and begin to drizzle in the boiling sugar mixture (which should be at approximately 245-250F, firm ball stage). When all of the hot sugar is added, turn the mixer up to medium high and beat until the bowl is no longer warm to the touch.
Add the butter one lump at a time and continue beating until mixture is smooth and fluffy, approximately 12-20 minutes. It will look rather like ricotta cheese for a while – just keep beating! Once it is smooth, scrape vanilla bean and mix in the vanilla specks (or use 1-2 tsp vanilla extract).
Keep at room temperature – do not refrigerate before it has been spread on a cake or cupcakes.