It's a typo and should simply say "quite astonishing".
After experiencing the severe recession in Italy, it was quite a astonishing to see shopping malls jam-packed with people buying like there's no tomorrow.
Source: Farewell Milan, hello Raanana - Israel Opinion, Ynetnews
Does "quite a astonishing" mean a lot of astonishing since we have "a" after quite? In addition to that, dictionary says that "quite a" is used before some nouns while in the above text we have an adjective. Shouldn't be "quite astonishing?"
It's a typo and should simply say "quite astonishing".
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
This sort of mistake is not uncommon on the web- people are often working fast and spellchecks don't catch them.
It could also be a more extensive typo: 'it was quite an astonishing sight'. But the smaller typo - an "a" slipping in, maybe because the phone rang while they were typing - seems more likely. (Note 'a[n]' can come before a noun or noun phrase.)
b