In a medium bowl, whisk together egg whites, cottage cheese, feta cheese, Monterey jack, peppers, spinach and salt.
Using a very small bowl (a custard cup, or a 5 oz ramekin will work well), press a 10- inch square of plastic wrap into the bowl, so the wrap is fully adhered to the sides of the bowl. There should be about 2 inches of plastic wrap left hanging over the edges of the bowl. Spray the plastic wrap in the bowl as well as the overhang, liberally with nonstick spray. Spoon the egg filling into the bowl, leaving 1/8’’ at the top. Form an air-tight bundle around the eggs; lift the sides of the plastic wrap on all sides just enough to twist the plastic wrap so that it encloses the egg. There should be no air in the bundle. Tie tightly with kitchen string, or a length of plastic wrap. Repeat with remaining filling, remembering to spray the plastic wrap each time.
In a large pot, bring 6 inches of water to a simmer (185 - 200°F.) There should be tiny bubbles rising to the surface; carefully drop all the egg parcels into the simmering water, and cook for 10 to 12 minutes, the centers should be completely set. Remove the egg parcels from the water with a slotted spoon and set aside on a plate lined with paper towels. Let sit for a minute until cool enough to handle. Using sharp scissors, cut the parcels directly under the kitchen twine; peel away the plastic wrap, the egg bites are ready to serve.