I’m not clear what is “retroactive” about what you call retroactive UX research. User research is studying users to inform the current or next design iteration, and this can occur at all stages in design-development:
To determine users’ characteristics, needs, goals, tasks, and work environment before making any designs or prototypes.
To test iterations of prototypes at increasing levels of fidelity to improve a design.
To summatively validate that the final product meets UX goals to justify release.
To test an established product (yours or competitor’s) to determine design improvements for the next version or generation.
All of these are “forward” user research.
You say you already have a product and you know the user’s goals. So if your intent is to tweak the design to improve the UX, then you can run your basic usability tests on the tasks that accomplish the goals and see where there are any problems.
Or perhaps by “laying the foundations,” you mean to do a major overhaul of the UX, or even create an entirely new product. The bigger the changes, the more abstract, qualitative, and naturalistic the user research becomes.
To do a major UX overhaul, you combine structured testing of specific windows/pages to accomplish specific tasks, with open-ended ethnographic research, observing in the real world how users use your product and how they accomplish the goals, with or without your product. You build an understanding of the product and the goals in context to figure out the UX you want to achieve.
To make an entirely new product, you go fully ethnographic, and start looking at the goals of the goals. Say one goal of your product is to “make international phone calls.” Start researching why people want to make international phone calls. Is it to stay in touch with overseas relatives? Are they planning international trips? Are they trying to acquire products they can’t get domestically? Look at how users pursue those meta-goals (with and without your product) to see where they succeed and fail. Start looking at how you can fulfill each meta-goal better. Survey technologies to find better ways of serving those meta-goals.
From your comment below, I see you're using "retroactive" to mean "after the fact" (i.e., doing the user research after the product was released). However, the above still applies: you're doing research to improve an upcoming, not previous, design; specifically, you're doing the 4th bullet above. It's still a matter of choosing how open-ended you want your research to be. Given your only foundation is the goals the developer assumed, then you are correct in that you in fact know very little about users, task, and environment. Thus, you probably should lean towards the ethnographic methods, if you have the authority and budget to make major changes to the product. No point in discovering a big unfilled need if you can't do anything about it.
