Pretty often when you brew an all-grain batch you get a quantity of extra wort with no apparent use. A common practice is to keep some of that wort for a starter for the next batch. Could someone instead process it into LME (by boiling it for some more time and storing it in a sanitised vessel) or, even better into DME (by other means) in order to use it as a fermentable in the future?
If you mean dry extracts, no. The previous poster has that covered. It requires freeze-drying and a bunch of other complicated stuff. However, you can make your own extract syrups. It's best not to think of them as LME OR DME at this point but more specific extracts (stout,pilsner,pale ale, etc.). Basically, all you do is mash out your grain and then boil it down until you get a thick syrup. You're just removing the water from the solution. Be sure you store it in sterilized airtight containers, though.
Is this efficient? Probably not. It's just as easy for me to do a full grain extraction every time i brew. For this to really be worth your time, you'd need to do 10-20 gallons of mash at a time and for that to be time-efficient, you'd need industrial equipment to boil off that much liquid, not to mention mash out that much grain.
In short, no. Any LME you end up with will be super-dark. Dry malt extract requires flash drying with high pressure nozzles and is not a home operation. Briess has some explanation of the process.
The technical nature of creating DME and LME is more than can be done in the home. It's even harder to do than malting your own grains, which is difficult enough, and requires a lot of specialized equipment.
Besides, a gallon of wort probably gets you less than a handful of DME.