Let me first briefly recapture the idea to avoid misunderstandings: You want to have a badge awarded to people who manage to ask a question that is challenging but well-asked (and in particular not difficult to answer due to being badly asked).
While I like the idea, I fail to understand why you require that the question receives an answer for the badge to be awarded (as least how I and some others understood it). If a question is really difficult, it might end up with no answer forever or at least for a very long time. And questions that remain unanswered forever due to being bad are mostly excluded by the score criterion anyway.
A few other aspects to consider:
I second Unihedron’s suggestion to allow for the question to have badly scoring answers. I would even go so far as to ignore answers with a score less than two (which is the requirement for bounties being auto-awarded).
There should be a time limit before first evaluating the badge conditions. This is to exclude questions that are very popular but comparably easy or inherently requiring rather long answers. Such questions could acquire the badge just by receiving upvotes faster than anybody can write a decent answer and not due to being challenging questions. Let’s also not forget that if there is a score criterion for the answers, people need time to vote on them too.
To make this limit somewhat adaptive to slower sites or tags, I would let it depend on the time a score of 10 was reached instead of the creation of the question. (As a side-effect, this would also attenuate the advantage for questions that only became good after editing.) Without being well-versed on the big sites and their time scales, I suggest two hours for now.
Questions that were closed at some time should not be eligible for the badge as they can be upvoted but not be answered during being closed. For example, if a question gets closed rather quickly for whatever reason and then is edited into a passable question, it may receive sufficent upvotes before being reopened. Also, this might be a way to game the system.
Asked a question that had a score of ten or more for two hours without attracting an answer scoring two or more or ever being closed.
As this is certainly more difficult than Nice Question and in analogy to Enlightened, I propose that badge to be silver (should the values remain that way). A gold version with higher difficulty suggests itself.