Preheat oven to 300°F (150°C) and place a baking pan filled with 1 inch of water on the bottom rack to create a humid environment.

Grease a 12-cup silicone muffin tin thoroughly with non-stick cooking spray.

Place eggs, cottage cheese, salt, and pepper into a high-speed blender.

Process on high speed for 30 to 45 seconds until the mixture is completely smooth and uniform.

Pour the egg mixture into a mixing bowl and fold in the shredded cheddar cheese.

Distribute the mixture evenly into the prepared muffin tin cups, filling each about three-quarters full.

Bake for 25 minutes or until the egg bites are set and do not jiggle in the center.

Remove from the oven and allow to cool in the tin for 5 minutes before using a plastic knife or spatula to gently release the bites.