This recipe makes a delicious, full-bodied ginger beer with a powerful ginger flavor, unlike many of the commercial variants.
Grate the ginger. This can be a lot of work by hand, but the ginger will grate far easier frozen. Otherwise, the grater tends to get clogged all the time. A grater attachment to a food processor works wonders. You will end up with around 4 c of grated ginger.
Blend ginger with 4 c hot water. Let the ginger soak for at least 10 minutes, mixing and mashing for the first few minutes. Squeeze out all ginger extract and strain.
This is your ginger extract--try it out in some tea!
Let sit at least 20 minutes so the ginger starch settles out. It's fun to play with, but you don't want it in your ginger beer. It's bitter and unsightly.
Hydrate yeast in 1 c water. Meanwhile, bring the extract and the other ingredients (minus 4 c water) to a boil. Add the reserved 4 c water and cool to below 80-85 F. Pitch yeast and bottle immediately. The beer should be ready in a few days. Keep an eye on the bottles or they will explode from over-carbonation. Swing-top bottles make checking easy--but do it over the sink!