Rehydrate the dried chilies, and to do so, pour boiling water over them and let them sit for about 30 minutes. Once they have softened, strain off and chop them up.
Mix the aromatics: Add chopped garlic, onion or shallots, chilies, lemongrass, galangal, shrimp paste, kaffir lime and coriander roots. Pound or blend them until the mixture is smooth, with a fragrant paste result.
Cook the paste: Take a non-stick pan and put it over the medium heat. Add little oil if you use water. Fry the paste for 5 to 6 minutes, stirring constantly, till the mixture becomes fragrant and has a tinge of caramel.
Tamarind and sugar: Add at the end tamarind paste and palm sugar. It will balance spiciness and sourness with a slight sweetness.
Store your paste: Allow your Tom Yum paste to cool and store it in a glass jar. If you used oil, you should keep it refrigerated for up to 2 weeks, or freeze for up to 3 months. If you used water, use your Tom Yum paste within a week.