I believe that asking the high-quality question is the best way to have a conversation. Asking the high-quality question is also the best way to learn about something or someone.
Asking the high-quality question is hard if you don't have context. It's akin to probing for the most important needle in the haystack, but you don't know what haystack it is nor a good idea of where the needle even is.
Despite not having context, one way to ask high-quality questions is to ask about trade-offs. Would you sacrifice some of X to get some more of Y? That usually reveals what people's preferences are.
Another great high-quality question to ask is to get to the heart of values. Sometimes it's a bit obvious to ask someone what their values are; instead, asking what someone would do if they didn't have to make money is a good way to suss out values.
Asking the high-quality question more often is a question that makes the other person spend time and reflect. It is not that the question is different, which it should be, but because the question reveals a thought-process or a bias someone had not recognized before.
The best high-quality questions are the ones that the recipient thinks about for a while. Those questions started something in an individual to self-reflect. Those questions allow for the transformation of a person's character.