Ah, in that case, you are probably encountering new problems every day, both specific and general. I would keep written notes about them, including what that are, how I addressed them, whether or not the resolutions were successful, and which ones I'm stumped on.
Include those passing "I wonder what to do" moments or questions in the list as well, rather than letting the thought fly from your head.
I'd bring that list to the meetings with the exec, and pick one or two from that to discuss with him -- starting with problems that I'm having trouble cracking.
If there are none of those, then I'd review one or two things I did, with an eye towards getting a perspective on how he would have addressed them and why that differs from my approach (if it does).
The odds are very high that doing this will lead the conversation to a fruitful, more high-level, discussion about how to approach management more generally, perhaps point out areas where I'm weak (we all have weak areas) and could use further study or training, and so forth.
Basically, I'd use a list like that as conversation-starters.