Preheat the oven to 350 degrees F. Grease and flour 2 baking sheets with 2 tablespoons butter and 2 tablespoons of flour. Mark parallel lines in the flour across the width of the tray about 4 inches apart. Put the eggs and sugar in a large mixing bowl, and with an electric mixer fitted with a wire whisk beat on medium-high speed until the mixture is pale yellow, thick, and has tripled in volume, about 8 minutes, using the mixer. Add the egg whites, remaining 3/4 cup flour, salt and vanilla, fold to mix thoroughly so the mixture is smooth. Fill a large pastry bag with a 3/4-inch plain tube with the mixture. Pipe fingers about 4 1/2-inches in length on to the baking sheet, using the lines as a guide. Dust the ladyfingers with powdered sugar. Bake until for 15 to 18 minutes, or until just firm on the outside and soft in the center