one big of a [noun]

Asked to comment on the use of the phrase “one big of a question,” I responded that it sounded totally off to me. I’ve always used a noun in the place of “big” here: one hell of a night, one humdinger of a lunch, one devil of a time, etc. Someone countered me with this link and the assertion that it indeed exists because it came up in the Google search. As far as I’m concerned, it’s existence on Google doesn’t automatically make it grammatical or acceptable, but I wonder if perhaps I’m missing something?

You are correct. That is not idiomatic.

While "that big of a [noun]" is commonly used, you can see from this Google Ngram comparison that usage of "one big of" is practically non-existent