Peel the dry outer layers of the lemongrass and discard them.
Roughly cut the bottom of each stalk (about 2 inches) and discard.
Finely slice the lemongrass stalks crosswise and set aside.
Roughly chop shallots, Serrano peppers, and galangal root.
Place all ingredients in a food processor or blender.
Process several times, and use a spatula to clean the side to make sure it's all mixed well until texture is smooth and pasty.
