Converting a seed junkie is a real skill and almost everybody fails at it the same way, so here is what actually works.
The core problem: parrots do not recognise food they have not seen before as food. It is not fussiness. A wild parrot that eats an unfamiliar thing dies, so they are hardwired to be suspicious. You are not persuading it that carrot is nice, you are persuading it that carrot is food.
What works, in order:
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Eat it in front of the bird. This is the biggest single lever and it costs nothing. Parrots are flock animals and they eat what the flock eats. Sit near the cage, eat a piece of the vegetable, be visibly pleased about it, do not offer any. Do this for a week. Mine started screaming for what I was having, which is exactly the point.
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Serve it the way seed is served. Chop it fine and mix a small amount into the seed at first — so little it is nearly invisible. Increase over weeks.
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Offer new food first thing in the morning, when the bird is hungriest, and leave it for an hour before the seed goes in.
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Warm and soft beats cold and hard. Cooked pulses, boiled rice, a bit of warm daal with no salt or masala. Mine took cooked chana before it would look at anything raw.
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Sprouted seed as the bridge, as post 2 says. Best trick in the book.
Timescale: months, not days. Mine took about four months from all-seed to eating vegetables properly.
And the safety rule that matters more than any of this. You must never starve a parrot into eating something new. A bird that stops eating for 24–48 hours is in genuine danger — their metabolism is fast and they have almost no reserve. "Take the seed away and it will eat when it is hungry" is advice that kills birds. Weigh the bird if you can, every few days, during any diet change. A drop of more than about 5% and you stop and go back to seed.
Never: avocado, chocolate, caffeine, alcohol, salt, onion, garlic, apple seeds. Avocado is the one people do not know and it can kill a parrot outright.
On pellets: good, and the same suspicion problem applies. Availability here is patchy and the price has gone silly, so I use them as part of the diet rather than all of it.