Preheat oven to 300°F. Line a 13- by 18-inch sheet pan (that has sides) with heavy duty aluminum foil. Pour on melted butter and spread out so that pan is evenly coated.
In a large bowl, use an electric mixer to beat egg whites and water until stiff peaks just start to form. Blend in sugar, cinnamon, and salt. Fold in pecan halves and spread mixture in a single layer onto prepared pan.
Bake for approximately 40 minutes, stirring and flipping pecans every 10 minutes. Watch nuts very closely during the last 10 minutes of cooking time, removing them from oven sooner if they are getting too dark. Nuts are done when they are mostly dry and golden brown.
Allow pecans to cool on pan until they are completely dry and crunchy, stirring occasionally to break them up. Store in an airtight container for two to three weeks (though they will never last that long!).
The pecan and egg white mixture will be very wet and goopy at first. Just do your best to flip the pecans and spread them back out into a single layer the first few times that you stir them. I find it helpful to clean my spatula between flipping them.
Feel free to add a pinch of cayenne for sweet and spicy nuts!