Just out of curiosity, I looked it up in an American dictionary and it does have a noun form over here, as well, but it's noted as "chiefly British, informal".

Although, the term "big ask" is something I'm certain I've used before, as well as others, but more in a business/corporate context.

Or maybe I've just watched a lot of British television?

I remember that phrase appearing seemingly out of nowhere 10 years or so ago. (UK)

Very weird. Maybe it had been percolating in business circles earlier than that. I don't tend to mix much in those circles.

I still want to believe it’s people dropping the “t” in “task”.

I’ve heard both phrases you mention a lot in American English too.