Preheat oven to 350 degrees F. Spread nuts in a single layer in a shallow baking pan. Bake for 10 minutes. Cool on a wire rack for 30 minutes. Meanwhile, reduce oven temperature to 325 degrees F. Grease a 15x10x1-inch baking pan; set aside.
In a bowl, whisk together egg white and water until frothy. Stir in granulated sugar, brown sugar, pumpkin pie spice, and salt. Stir in cooled nuts. Spread nuts in a single layer in the prepared pan.
Bake about 20 minutes or until nuts appear dry, stirring once halfway through baking. Transfer nuts to waxed paper, separating into individual pieces or small clusters; cool completely. Divide nuts among clear gift bags. Tie bags closed with string and place in tins.