Bash the lemongrass stalks with a rolling pin and remove the woody outer layers. Finely chop the softer inside stalk and add to a medium saucepan.
Grate the ginger into a sieve (strainer), set over a bowl. Use a spoon or spatula to press the ginger into the sieve, extracting all of the juice into the bowl below. You should get around 4 tbsp of juice. Add the gi