Spray a 6 or 8qt slow cooker with non stick spray, then add the nuts.
Drizzle the maple syrup over the nuts and stir well, then add the sugar, 1/2 cup of brown sugar, and the apple pie spice and stir to combine.
In a small bowl, whisk the egg whites until frothy and just barely holding a soft peak. Fold the whipped egg whites into the nuts.
Place the lid on the slow cooker and cook for 2.5 hours stirring approximately every 45 minutes.
After 2.5 hours, lift the lid, add the water and the remaining 1/3 cup of brown sugar and stir. Replace the lid and cook for another 20 minutes.
After 20 minutes, stir the nuts and turn the cooker to high. Cook for 20 minutes longer.
Line a baking sheet with parchement paper or a silicone liner and pour the nuts onto the pan. Spread them out and immediately sprinkle with a bit of salt.
When the nuts feel dry to the touch and have hardened, break them up with your fingers. Place a cooling rack on a baking sheet and transfer the nuts to the rack. This will help them finish drying.
When the nuts are fully dry, move them to an airtight container. They should keep several weeks in a cool, dry place.