Combine sugar and water in a heavy saucepan. Cook over medium heat, stirring constantly, until mixture is clear. Cook, without stirring, until syrup reaches soft ball stage or candy thermometer registers 240° (about 10 minutes).
While syrup cooks, beat egg whites at low speed with an electric mixer until foamy. Add cream of tartar and salt; beat at medium speed until soft peaks form. Increase to high speed, and add hot syrup in a heavy stream. Add marshmallows, a few pieces at a time. Beat until stiff peaks form and frosting is thick enough to spread.