Heat a cast-iron skillet over medium-high heat. Place the shallots and garlic in the skillet and dry-roast until browned and blackened on all sides, about 5 minutes. Remove from the skillet and set aside to cool slightly
Meanwhile, place the skillet over medium heat, add the dried chiles, and dry-roast, turning and moving them frequently, until they start to give off an aroma; they should not blacken or burn-just heat gently until they are dried out and brittle. Alternatively, you can roast the shallots, garlic, and chiles over a charcoal or gas grill
Transfer the chiles to a mortar and pound them to a powder (discard any tough stems). Add the galangal and a pinch of salt and pound to paste. Transfer the mixture to a small bowl and set aside. Alternatively, place the chiles and galangal in ablender or food processor and chop them as fine as possible
Slide the peels off the shallots and garlic and discard. Coarsely chop the shallots, palce them in the mortar with a pinch of salt, and pound to a smooth paste. Add the paste to t he mixture in the small bowl, then place the garlic cloves and a pinch of salt in the mortar and pound to a smooth paste. Add all the pounded ingredients to the mortar and pound together. Alternatively, add the shallots and garlic to the food processor with a pinch of salt and process
Add the fish sauce and 2 Tbsp of the warm water and pound or stir to blend well. The paste should be very moist and smooth: add a little more warm water if you wish. Taste for salt and add a little more salt or fish sauce if you wish. Stir in half the coriander
Transfer the sauce to a small bowl. Sprinkle the remaining coriander over the top. Serve at room temperature. Store leftovers in a sealed contained in the refrigerator for several weeks