This is a no-water added method of making syrup. The brown sugar and ginger both become very mild, so not only can they be used in drinks, but can be used as brown sugar syrup too. For the honey version, see Recipe ID: 1670183.
To make it even easier (The method and tips are in the last half of the recipe)
enough to cover the ginger
Finely julienne the ginger. If the skin bothers you peel it off first. Slicing the ginger is fine too, but if you julienne it more juice will come out easily.
Put the ginger, brown sugar and mizuame in a bowl and mix. At first there may seem to be too much brown sugar, so you may wonder whether it will turn into syrup...
...but if you leave it for a while, the juices come out of the ginger and it turns into a brown sugar syrup. Mix up up occasionally and wait until the brown sugar dissolves completely (1 to 2 days).
If you are going to use it all up right away you're done. Just make sure that the ginger doesn't poke up above the syrup (to prevent it from molding).
If you want to keep it for a while, after plenty of ginger juices have been exuded, heat up the syrup to disinfect it. If you do this it's a good idea to have the mixture in a heatproof container to begin with.
If you mixed it up in a heatproof container, put it in the microwave and heat it through until it's bubbling to kill off any bacteria. Watch it so that doesn't bubble over.
You can transfer it to a pan and heat it through that way too.
You can leave the ginger in the syrup, or take it out. If you are taking it out, it's easier to do so when the syrup is hot and not so sticky.
The amount of juice that comes out depends on the ginger, but if you use the amounts indicated in this recipe you should end up with a light syrup which won't solidify easily even when refrigerated and is easy to use.
If you prefer a thick syrup, reduce the amount of ginger, or reduce the syrup a little by heating it. The syrup in the top photo uses a bit less ginger.
This is the brown sugar syrup that I used as reference for the ratio of ingredients. Cookpad user La Lande's "Homemade Brown Sugar Syrup That Won't Re-Crystallize (Cinnamon Flavored)" - (Recipe ID: 801145)
Easy version: Use whatever amount of ginger you like, and enough brown sugar to bury the ginger. You can make it in the same way as above. (It's easy, but less likely to re-crystallize.)
The flavor will change depending on the ratio of ginger to brown sugar. You can use the ratio you like, but if there's too much brown sugar it is more likely to crystallize.
One Cookpad user made "Sake lees drink with brown sugar and ginger syrup" (Recipe ID: 2057199).
"Ginger In Honey (for tea) " - (Recipe ID: 1670183) is easy and delicious too.
Story Behind this Recipe
There are many recipes out there for brown sugar and ginger, but I wanted to make a version that was as concentrated as possible easily. I used to make this the "even easier" way, but ever since I encountered Cookpad user La Land's brown sugar syrup I've been adding mizuame to mine too. This is how I've been making this several times since last year.
The amount of brown sugar that will melt in the juices that come out of the ginger is limited. If you use the "easier" method in particular, the lower the humidity the harder it is for the sugar to melt. You can just stir it up from the bottom of the jar before using, or put the jar in hot water to warm it through, and any crystallized parts will melt.