Method 1. Using a food processor

1. Prepare the chilis. Remove the seeds using kitchen gloves. The heat from the seeds is potent and can burn your skin and cause discomfort for hours. Soak the chilis in hot water for 10 minutes. 20 minutes in warm water. Or until the chilis are soft. Drain the water and pat dry the chilis. 
2. Toast the dry spices. Dry toasting the white peppercorns and coriander seeds. Once cooled, grind in a spice grinder into a powder form. 
3. Add all the ingredients into a food processor and blitz away until you get a fine paste. Pause a couple of times to scrape the edges of the food processor with a spatula. Add more water as needed, but not too much. 
4. Remove and use immediately for cooking. Store any leftovers in an airtight container in the refrigerator for up to one week and 3 months in the freezer—no need to fry your Tom Yum paste, especially if you will use it immediately. 

Methods 1. Using mortar and pestle

1. Prepare the chilis. Remove the seeds using kitchen gloves. Soak the chilis in hot water for 10 minutes or 20 minutes in warm water until the chilis are soft. Using about one cup of warm water is all you need for soaking the chilis. Drain the water and pat dry the chilis. 
2. Toast the dry spices. On medium heat, dry toasting white peppercorn and coriander seeds until fragrant, 3-4 minutes. Do not let the seeds get too browned, or they will release a bitter, unpleasant taste. Remove from the pan and let cool for 5 minutes. Once cooled, grind in a spice grinder into powder form. Set aside until ready.
3. Add the chilis and salt to a mortar and pound until a smooth paste forms. Be careful with the pepper pieces jumping at you, especially your eyes. See notes for how to prevent this from happening. 
4. Add the lemongrass and galangal. These two ingredients are the toughest and most fibrous ones on the ingredient list. Pound these away until a smooth paste forms. This will be your hardest part about using the mortar and pestle. The best part? It's downhill from here and goes by pretty quickly after these two. 
5. Add shallots and garlic. Pound away to a smooth paste. Are you getting your forearm workout yet? (; 
6. Add cilantro stems, kaffir zest or leaves, and the ground-up spices. Grind to paste.
7. Add the tamarind paste and use the pestle to stir to blend the ingredients in the paste form together. 
8. And finally. The only thing left at this point is the shrimp paste! Add the shrimp paste last and grind together well with your pestle. The shrimp paste is the softest ingredient on the list and should be the final item added to the mortar and pestle. It helps bind all the ingredients together into a smooth, soft paste.