Preheat oven to 350 degrees F. Spread almonds in a single layer in a shallow baking pan. Bake for 10 minutes. Place on a wire rack; cool 30 minutes. Reduce oven temperature to 325 degrees F. Grease a 15x10x1-inch baking pan; set aside.
With a wire whisk or rotary beater, beat egg white and water in a large bowl until frothy. Stir in granulated sugar, brown sugar, pumpkin pie spice, and salt. Stir in cooled nuts. Spread nuts in a single layer in 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.
Place almonds in tightly covered decorative containers. Cover and store in the refrigerator for up to 1 week. Makes 5-1/2 cups.