Heat the butter in a 20 cm frying pan on medium high until melted. Beat together the eggs and milk. Season with salt and pepper. Pour into the pan and cook for about 1 minute or until it starts to set.
Use a spatula to gently pull the egg from the outside in, tilting the pan for some of the raw egg mixture runs from the centre to the outside of the pan. Repeat once more on the opposite side. Cook until most of the egg is cooked through.
Spoon ½ the cottage cheese and ½ the bacon in a line down the middle of the omelette. Fold both sides of the omelette over the filling to enclose.
Transfer to a plate and top with the avocado and the remaining cottage cheese, bacon and basil.