I'm interested in the history of the Greek peninsula under Roman rule from anywhere between the 1st and 7th centuries CE. This could be anything pertaining to social, economic, administrative or intellectual history.
There actually isn't one, at least not a comprehensive one. I would start with Chaniotis (below), then check out Engels on Roman Corinth. Corinth is a good focus because it has been well-excavated. It can serve as an exemplar of the rest of the Greek peninsula (usually), with the caveat that Corinth got a lot of special attention from the Romans compared to other Greek cities. Then check out Alcock, who is extremely smart. I'd want you to look at Chaniotis first, though, then Alcock.
Chaniotis, A. (2018). Age of conquests: The Greek world from Alexander to Hadrian (336 BC-AD 138).
Engels, D. W. (1990). Roman Corinth: An alternative model for the classical city. Chicago: University of Chicago.
Alcock, S. E. (1993). Graecia capta: The landscapes of Roman Greece. Cambridge: Cambridge University Press.