Line a 9×5-inch loaf pan with parchment paper, leaving an overhang on the sides for easy removal.
In a medium saucepan, combine honey, sugar, and water. Bring to a boil over medium heat, stirring occasionally.
Continue to cook the mixture until it reaches 260°F (hard-ball stage) on a candy thermometer, about 20 minutes.
While the honey mixture is cooking, in a separate bowl, beat the egg whites with salt until stiff peaks form.
Once the honey mixture reaches the correct temperature, remove from heat and gradually pour it into the whipped egg whites, beating constantly.
Stir in the vanilla extract, chopped almonds, hazelnuts, candied orange peel, and candied lemon peel.
Pour the mixture into the prepared loaf pan, smoothing the top with a spatula.
Let the torrone cool to room temperature, then refrigerate for at least 4 hours or overnight until set.
Using the parchment paper overhang, lift the torrone out of the pan and place it on a cutting board.
Dust the top with powdered sugar and cut into small rectangular pieces.
Serve and enjoy the traditional Italian torrone!