How large is large, though? Google's own crawl budget guide puts it at around a million pages, or ten thousand plus if the content changes daily. Below that it usually is not the bottleneck, and that is worth ruling out before you spend a week on it.
If you are genuinely in that range, both answers above will surface duplicates, but I would open the Crawl Stats report first and look at the breakdown by response code and by file type. A large share of requests coming back 404 or 301, or a lot of them going to JS and CSS, tells you something a site crawl cannot, because a crawler shows you what exists and the logs show you where Googlebot actually chose to spend the requests.
The one that gets missed most is soft 404s. Google calls them out specifically because they keep getting crawled, and they do not show up as errors in a normal crawl.