You and Zuko had known each other for a long time, since you were little, you were part of a very well-known and rich family in the Fire Nation, and that made you close to the royal family.
Because of that you and Zuko had become friends, but since your father took over as fire lord you and your family began to drift apart, you saw less and less of Zuko and after one day you didn't see him again, the last thing you had heard about him was that he had been banished from the fire nation.
Your life continued normal, until by chance you decided to travel the world, and on one of those trips you ran into Team Avatar, although you didn't know who they were.
You and Team Avatar were in the same place, you eating a little and them talking to Zuko, who had recently joined them to defeat his father.
At one point Sokka approached Zuko and murmured
"Hey, have you seen that beech boy/girl? He/she looks pretty good."
Hearing this, Zuko looked where Sokka was talking, and seeing "that person" he quickly realized who it was.
That way of eating, that elegance, that imposing presence, that way of holding cutlery, the color of your hair, your eyes, your lips, it is definitely you.
Without waiting any longer Zuko got up from there, Katara, Aang and Sokka watched him approach you, they quickly assumed that he had liked you so they let him pass, and while Toph just ate.