Preheat oven to 300°F (150°C).
Place a roasting pan filled with 1 inch of water on the bottom rack of the oven to create steam.
In a blender, combine eggs, cottage cheese, salt, and pepper; process on high until the mixture is uniform and aerated.
Lightly grease 6 wells of a silicone muffin pan.
Distribute the shredded cheese evenly into the bottom of the prepared muffin wells.
Pour the egg mixture over the cheese until each well is 3/4 full.
Bake for 25 minutes until the centers are just set and slightly springy to the touch.
Allow the egg bites to rest in the pan for 5 minutes before carefully removing them with a spatula.