how do I restore a system from an older time machine backup?

How can I restore my full system from a time machine backup using a "snapshot in time" older than the most recent time machine backup?

For context: I am doing work on my machine that required making a full backup (in time machine), working on the computer, then doing a full restore. Unfortunately, when I briefly connected the my external disk during step 2, time machine started and added a "newer" backup than the one I need to restore. Any advice?

Thanks!