Choose a large stainless steel or heatproof glass bowl that will fit over, not in, a medium-size saucepan. Fill the pan with about one-inch water and bring to a simmer.
In the bowl, off the heat, combine the maple syrup, sugar, egg whites, and salt. Place over the simmering water and beat with a handheld electric mixer until the frosting is fluffy and stands in stiff peaks, about 6 minutes.
Remove the bowl from the water and beat for about one minute longer. Beat in the vanilla. Use immediately to frost cooled cake layers.