This was one of the first infusions that I created. I had some leftover ginger and I needed to use it before it went bad. So I mashed it up and threw it in a bottle of vodka. What resulted was absolutely fantastic. This is an infusion that I have never seen anywhere in a liquor store, but it is light, aromatic, and mixes amazingly well with just about everything else. The thing about ginger infusions is that it works much like the actual root. I can be used in almost any type of application.
We tend to want to break foods down into limiting categories. A food either tends towards sweet or savory applications. It's good in either earthy, or light flavor combinations. It's rich, or delicate. Anyone who has experimented with food knows that these categories are often limiting. Chocolate is as excellent in a mole as it is in a custard. Coffee rubbed burgers are as rich and amazing as any mocha. That said though ginger breaks these boundaries before we can even set them up. Ginger ale is probably one of the lightest, sweetest and most classic uses of the root one can think of. Ginger snap cookies however are deep and earthy, with the richness of molasses and the infusion of other spices. Ginger in curries is deep and savory, but aromatic and excellent.
Ginger as an alcoholic infusion is similar. Mixed with simple white syrup it produces an amazing delicate sweet product that will lighten any dessert drink. It mixes well with certain fruit liqueurs such as apple, or even peach. Mixed with turbinado syrup it becomes a deeper liqueur ideal for mixing with Amaretto, or coffee and cacao liqueurs. Without any sugar it can provide an accent to gin drinks, and other herbal applications. It is probably the most under appreciated, dynamic infusions available.
Ginger is impossible to over infuse much like fruit. I have left the root in Rum for over a month with no negative side effects. At the same time I have found most ginger infusions are useable after only a couple days. You want to cut your ginger thin and break up the slices a bit in a mortar and pestle. The mortar step isn't strictly necessary, but it will speed your infusion considerably. I peeled my ginger before infusing it for a long time, then saw some ginger infusing in vodka at an Asian restaurant with its skin still on and decided to give that a try. I didn't notice any adverse flavor effects from leaving the skin on the ginger. So I recommend not skinning as it does add quite a bit of work to the process.