Combine first 4 ingredients in a large heavy saucepan.
Combine egg yolks and next 3 ingredients. Gradually stir into brown sugar mixture.
Cook over medium heat, stirring constantly, until mixture thickens and boils. Boil, stirring constantly, 1 minute. Remove from heat; stir in 1 teaspoon vanilla. Pour into pastry shell; set aside.
Combine 1 tablespoon cornstarch and cold water in a small saucepan, stirring until smooth. Stir in 1/2 cup boiling water; cook over medium heat, stirring constantly, until mixture thickens and boils. Boil, stirring constantly, 1 minute. Remove from heat; cool completely.
Beat egg whites at medium speed with an electric mixer until foamy. Combine 3 tablespoons sugar and baking powder; gradually add mixture to egg whites, 1 tablespoon at a time, beating until stiff peaks form and sugar dissolves (2 to 4 minutes). Add cornstarch mixture, salt, and remaining 1 teaspoon vanilla; beat until blended. Spread meringue over warm filling, sealing to edge of pastry.
Bake at 325° for 25 to 28 minutes or until golden brown. Cool.