Soften gelatin in cold water in a small mixing bowl. Scald 1/4 cup plus 2 tablespoons whipping cream; add to softened gelatin, stirring until gelatin dissolves. Chill until mixture reaches consistency of unbeaten egg whites.
Combine remaining whipping cream, sugar, salt, and vanilla in a large mixing bowl; beat at medium speed of an electric mixer until soft peaks form. Beat chilled gelatin mixture until frothy; fold into whipped cream mixture. Gently fold in chopped peaches. Chill.