The Thai way of making a paste is always by mortar and pestle, by tradition. The mortar and pestle is part of the essential Thai kitchen, along with pots and woks, graters and knives.
Each ingredient is added gradually, a bit at a time, in a given order of hardest and driest, to softest and wettest. Each ingredient should be reduced to pulp before adding the next ingredient. Once each is added and pounded, they release their fragrance. The balance of the paste is judged by this aroma and is adjusted in the making process. As with all Thai cooking, recipes are a guide, and are adjusted at the time of preparation, trying to achieve balance of salty, sweet, sour and hot.
By using a mortar and pestle, you not only can make the paste, but you vary the texture to be coarse or fine, with bits in if you like. Or completely smooth. It is much easier to make exactly the right consistency that you wish, with over doing it, which or course can be easily done in a food processor. Many claim that the taste is superior of a smashed, grounded and pounded paste to that of a sliced and diced machined version.
(This is adapted from, David Thompson’s, Thai Food(2002), which is an amazing collection of Thai cuisine, history, culture and society, regions, pretty much everything you need or could ever want to know about Thai cooking.)