Toast the coriander seeds in a dry pan over medium heat for 1–2 minutes until fragrant and just starting to darken. Let cool.
Add all paste ingredients — Thai green chilies, shallots, garlic, chopped galangal, lemongrass, kaffir lime leaves, cilantro stems, toasted coriander seeds, and salt — to a blender or food processor.
Add 2 tablespoons of water and blend into a rough paste, scraping down the sides as needed.
Add the third tablespoon of water only if needed to get things moving. The paste should be thick and fragrant, not watery.