Start by finely chopping the cabbage into strips, then transfer them to a large bowl. Add enough water to cover all of them and the vinegar, let them soak for 10 minutes.
Now finely chop the onion into strips and transfer them to a bowl, squeeze the lime all over them and mix. Set aside.
Grate the carrot and set aside, finally, chop the boiled eggs into thin strips.
Next, into a large bowl, add the grated carrot, the eggs, the cabbage with the water previously drained, the onion strips and season with the dried parsley, the white vinegar, the sugar, and the salt, mix all the ingredients very well.
Now add the mayonnaise and mix well until creamy.
Serve.