Place 1-¼ cups of sugar, the water and salt in a saucepan over medium high heat. Stir until it comes to a boil then stop stirring and attach a candy thermometer to the side of the pot. You will let the syrup boil until it reaches between 238°F to 245°F. 

While the syrup boils, place the egg whites and cream of tartar in a mixing bowl. Stir to incorporate the cream of tartar and keep the mixer on low speed. 

Keep an eye on the candy thermometer. When the syrup reaches 230°F to 235°F, switch the mixer to medium-high speed to whip the egg whites. Slowly add the remaining ¼ cup sugar and continue whipping until the egg whites reach medium soft peaks (when you lift the whisk, the meringue should create a pointed peak then slowly droop back down). 

As soon as the syrup reaches between 240°F to 245°F, remove it from the stove and slowly drizzle the syrup into the meringue. Keep the mixer on medium to medium-high speed while you drizzle in the syrup and avoid getting the syrup on the edge of the bowl or on the beaters. 

Once all the hot syrup is added, pour in the vanilla extract and beat the mixture on high speed for 1 to 2 minutes. You can pipe the meringue while it is still slightly warm but if you want to use it to make buttercream, wait until it cools completely.