Heat a nonstick pizzelle iron. In a large bowl, sift together flour, baking powder, and salt; set aside. In a large bowl, whisk the eggs. Slowly add the sugar and continue mixing until well blended. Whisk in the extracts. Slowly add the cooled butter in a steady stream, whisking continuously until the batter is smooth. Slowly add the sifted flour mixture, and keep whisking until the flour is completely incorporated into the batter. Be sure not to over mix. Fill a pastry bag fitted with a #4 Ateco plain tip (see sources) with batter. Pipe 1 1/2 tablespoons of batter in a circle around the center of each pattern on the heated pizzelle iron. Close the iron and seal with the clasp. Cook for 50 to 60 seconds. Using a small spatula, remove pizzelles, and place on a wire rack to cool. When pizzelles are cool, if necessary, trim to original pattern. Spread half of the cookies with 1 1/2 tablespoons of cooled caramel sauce, and sandwich together with a plain cookie, pressing gently to evenly spread caramel. Store in an airtight container up to 3 days.
In a small saucepan, combine sugar, water, corn syrup, and lemon juice over medium heat. Gently swirl until sugar dissolves. Without stirring, cook mixture until dark amber in color, swirling pan carefully while cooking, about 10 minutes. Reduce the heat to low and slowly add the cream, stirring with a wooden spoon. Be careful, the hot caramel will sputter when the cream is added. Add the vanilla bean and the butter, and stir until the sauce is smooth. Strain the sauce through a fine strainer into a bowl, and set aside to cool. Yield: about 1 cup