I found a few articlescand threads on Dutch sites about people feeding cooked parsnip to their parrots. Though I think I remember reading that not everything that's safe for parrots, is also safe for tiels to eat?
Judging from my gut feeling alone, I would say it is probably safe. Parsnip is a root plant, closely related to carrots. Since carrots are safe to feed your tiel, I would think parsnip is too