sparrowsong98
Hmm, that's annoying. It's hard to know why they still refuse to eat vegetables, though it's likely that their parents and any other birds they had been around didn't eat fresh vegetables, either. Maybe a video of finches eating vegetables (or better yet, real birds) could convince them to eat the vegetables.
Maybe they don't like the texture, considering that they've been eating dried seed. Perhaps you could try giving them dried vegetables by crumbling it over their seed. Even better, get some vegetable pellets for budgies and other small birds. These should look more like their seed. Broccoli could also be better for this reason, as the florets are a similar shape to seeds, and the idea of picking them off is kind of like spray millet.
You might be able to convince them to eat it by providing strands of greens that they can use as nesting material. Mush up the ends of the vegetable so the bird tastes the juice when it picks up the leaf. This would increase the chances that the bird would figure out that vegetables are edible.
The birds might not associate the colors of vegetables with food, as most seeds and eggfood are a plain yellow color. Try switching out the food dish for a dark green one, and remove anything else in their line of sight that is green. After a couple of weeks, give them green vegetables in the green dish, or remove the dish for a few minutes and clip greens on the side of the cage where the dish was. They might be more interested in eating greens after that.
Getting them to eat new food will probably be most successful with a combination of approaches. Also check out articles on how people get their picky kids to try new foods (especially those involving hypersensitive or autistic kids). Some of the ideas could be applicable to your birds.