Add egg whites, cottage cheese, 1/4 cup of the shredded Monterey Jack cheese, flour, dried basil, garlic powder, salt, and pepper to a blender. Blend until smooth, about 15 seconds.
Pour or ladle the mixture evenly into the muffin cups, filling each about 3/4 full. Sprinkle the remaining 1/4 cup of shredded cheese over the egg cups.