I have found that correcting change basal needs with a CGM to be 'approaching' easy. Check the activity profile of your insulin and review how long it is active in your system. Most users say that humalog (the insulin I use) last for 4 hours and peaks in 2 hours. check out the first post by Tim on this page: https://forum.tudiabetes.org/topics/lantus-vs-humulin-n.
Since my humalog peaks in 2 hours, I always go back 2 hours before the problem time. If I noted that my BG was dropping below my target range at 2PM, then I would adjust my noon basal rate down and monitor. Notes: a small basal change can have bigger changes then you expect. I recomend changing the minimum and reviewing your results. I like to wait 3 days before further changes as, I am sure you know, every day has its own variablility.
It is great that you are trying to figure this out as I hope every insulin user reaches this point. We simply can't wait for the next 3 month appointment or for the CDE to get back to us. Please be aware that you are aiming at an invisible, moving target called T1D. Your rates can and will change in ways that do not make sense and are unexpected- there are just to many factors to consider (weight loss/gain, carb intake, fat/protein intake, exercise, stress, digestion, etc.) Do not beat yourself up if you adjust inaccurately or not enough. Keep working at it. I often find it is like the children's game whack-a-mole - you correct your post-breakfast BGs and then your nighttime BGs are out of whack for unknown reasons. Most importantly, keep an open mind and be ready to adjust your basals/boluses logically and reasonably.