I found a search term – reefing mirror dinghy.
Shortening sail is the term for when there is too much wind. On a ship with many sails, this is done by reducing the number of sails offered to the wind. On a sloop or any small boat with only one or two sails (jib and main), the sails are reefed – only a part of their surface is offered to the wind, in order to de-power the boat and make handling easier.
There are two methods of reefing, roller and slab. The method described here is called slab reefing. The jib on a modern boat is furled around the forestay, and some boat designs allow the mainsail to be furled around a revolving boom.
Normally, it is not possible to reef a Mirror dinghy sail for two reasons. Most Mirror mainsails are not made for it and there is the problem of keeping the gaff close to the mast.
Here is a reminder of the Mirror rig:
If the gaff pulls too far away from the mast, it leads to increasing difficulty in trimming the sail. The solution is some kind of lashing that is loose enough to allow the gaff to slide up and down as a sliding gunter.
This is a nice design for the lashing as it can be controlled from lower down on the gaff and cleated. Once you have a reefable sail (they can be found, or a sailmaker can adapt your non-reefable sail), and the problem of the gaff is solved, then you can look into your method of reefing. The most convenient is single-line reefing. Here is a nice young Australian showing us how it is done, but it should be realised that our friend from down-under has a Bermuda rig with no gaff problem:
I have followed this method, and it seems to work well. Of course, to do this kind of manoeuvre at sea, you need to be able to lash the helm once you have hove-to – because you do need both hands to release the main halyard to the mark and then take in the reefing line. It’s delicate in a dinghy, but it can get you out of a tight spot when the wind gets up. It also gives the boat lee helm making it easier to tack without getting “clapped in irons” (facing the wind without steerage), even when you have to take the jib down.
Here’s another method making it possible to drop the mainsail at sea.