Use a fine microplane grater to grate ginger into a large jam jar. Mix in remaining ingredients.
Alternatively, puree all ingredients together in a blender or food processor.
Use as is, or, to make more like a syrup texture, strain the mixture through an extra fine sieve, squeezing as much liquid out of the pulp as you can. Pour into an airtight container and store in the fridge for up to one week. Stir well before using.