Heat butter over medium heat about 5 minutes. Remove from heat and allow to cool to room temperature. In a small bowl, whisk together the flour, baking powder and salt. Beat eggs and sugar at medium-high speed until thick and pale yellow, about 2 minutes, then mix in vanilla. Sift flour mixture over the top of egg mixture and fold in, using 3 additions. Fold in the cooled melted butter in 3 additions. Let rest for at least 30 minutes. Preheat oven to 450°. Generously butter 2 (12-mold) madeleine pans. Fill the molds 3/4 full with batter, leaving the batter mounded in the center. Bake about 8 to 10 minutes, until the cakes are golden on top with golden brown edges. Immediately unmold each cake onto a rack to cool. Dust with powdered sugar, if desired, when serving.