Use a stand mixer. It will change your life. You can make this using a hand mixer, but it just takes time. In a clean bowl (any grease on your bowl or utensils will ruin the icing -- egg whites hate grease!), beat the egg whites and salt on high speed until foamy.
With the mixer still running, slowly add the sugar. Beat mixture until soft peaks form. When pulling the mixer out of the white mixture, you should get a little point that bends over.
Bring the corn syrup to a boil over medium heat in a small saucepan. When the corn syrup comes to a boil, remove from heat.
Slowly pour the hot corn syrup into the egg mixture while your mixer is mixing on high. Beat the mixture until stiff peaks form, about 5 minutes. Add the vanilla, and mix to combine.
Use right away.
Video
Notes
Use the frosting right away and eat any leftovers, as it doesn't store well.
You can leave a cake that has been iced with this icing uncovered, since any type of plastic wrap on it will be a mess.
Add the sprinkles as soon as you are done spreading the icing. A thin crust will form, and the sprinkles won't stick if you wait too long.
This recipe doubles well.
This is enough to frost 18 cupcakes or the outside of one layered cake. This is not a great icing to fill a layer cake. The cake kind of smashes it into nothing, and you don't have a nice layer in the middle anymore.