Her parents could not afford the operation when she was a child, and now any money her mother earns is needed for her father, who is in hospital with complications from diabetes.
The Honeys set about raising money to bring her to New Zealand for surgery, but what followed was a "year of dejection" during which request after request for help was turned down. Things changed when they contacted Takapuna facial surgeon Mark Izzard on Facebook, however. He replied within five minutes, offering to operate without charge.
That left the Honeys to raise money for the airfares and organise a health visa, a challenging task in itself. Rotary got on board, as did an organisation called Romac, set up to help disfigured children.
Then, when most of the pieces were in place, the couple returned to Komodo, but couldn't find Ani. On their last day there a local rode around the island on his motorbike, door-knocking until he tracked down her mother in another village. Soon the 20-year-old was connected with the Honeys via Facebook.
Ani Budjen said she had feared the growth would turn cancerous. It also made her shy with other people.
"My friends like me for who I am but other people, sometimes they look at me and don't like me. They are always asking me, what's that on your face?" she said.
She had planned to start saving for an operation once she finished her studies.
At first she was unsure whether to believe the Honeys' offer was genuine, but once she landed in Auckland things happened quickly. She was barely off the plane when she had her first operation; she has had three so far, to cut out the growth and replace it with skin grafted from behind her ear, and has one more to come. The skin is scarred now but will eventually return to its normal colour.
Ani said she was grateful to the Honeys, and the roughly 30 other people and organisations who had helped, ranging from Dr Izzard to Rotary clubs in Kerikeri, the Bay of Islands and Takapuna, even a man in Sweden.
"I think they're awesome because they want to help another person they don't know," she said.
"They work hard to help me and want me to come here. It is my best experience. I can't forget this."
She would go back to Indonesia a changed person.
"We live in this world not just for ourselves, we have to give a hand to others. That's what I've learned," she added.
The keen baker had also learned to make pavlova, seen the big kauri in Waipoua Forest, cruised the Bay of Islands on The Rock, seen Russell's Birdman Festival and made lots of friends.
The highlights of her five-week stay, however, had been simple things like walking the family dog and being greeted on the streets of Paihia by her new-found friends.
She returns to Indonesia on Tuesday next week, and, after catching up with her family, she will start her third year of a four-year management and accounting degree in Yogyakarta, a city on the island of Java.
The Honeys founded The Rock Overnight Cruise in Paihia.
They sold the business to finance projects in Indonesia such as a pool for poor city children, a research institute and an Outward Bound-style outdoor education centre.
They are currently helping a blind boy from Komodo with a serious skin condition.
