Preheat oven to 375 degrees. Butter and flour madeleine pans carefully.Advertisement
Melt butter and let it cool.
Beat eggs, salt, and sugar together until thick, about 8 minutes. Add vanilla. Fold in flour, rapidly but gently. Fold in butter gently, but make sure it does not settle to bottom. Quickly spoon mixture into madeleine pans. Bake until golden, about 10 minutes. Remove from pans. Cool on racks.