Combine sugar, water, and syrup in a small Dutch oven, stirring well; cook over medium heat, stirring constantly, until sugar dissolves. Cover and cook 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, without stirring, until mixture reaches soft crack stage (280°).
Cook honey in a small saucepan over medium heat until thoroughly heated. Add honey to syrup mixture, and continue cooking until mixture reaches soft crack stage (290°).
Beat egg whites (at room temperature) in a large ovenproof mixing bowl until stiff peaks form. Add hot syrup in a thin stream, beating constantly at high speed of an electric mixer. Place mixing bowl in boiling water, and continue beating until mixture is stiff and holds its shape. Stir in chopped almonds, pistachios, and vanilla.
Press mixture evenly in a buttered 13- x 9- x 2-inch baking pan that has been sprinkled with cornstarch. Cover mixture with buttered waxed paper; place another 13- x 9- x 2-inch baking pan on top of waxed paper. Weigh down top pan with a heavy object. Let stand overnight to set.
Cut candy into 1-inch squares; wrap individually in waxed paper or colored cellophane, if desired.
Note: Honey-Pistachio Nougat squares may be dipped into melted chocolate, if desired.