In a food processor or blender, process the ingredients in the following order, one at a time, sprinkling with a bit of salt to help break them up: lemongrass, galangal, chiles, lime leaves, shallots, garlic, and soy sauce. Blend until each ingredient is totally incorporated before adding the next, stopping as needed to scrape down sides with a spatula. You should end up with a thick, semi-dry paste.
In a wok or skillet, heat the oil over medium-low heat until shimmering. Stir in the curry paste and cook until the oil is combined and the mixture is very fragrant, 5 to 10 minutes. Kris notes that this step, "helps the paste keep longer and become more hom (the Thai word for the savory fragrant aroma that happens when you toast/roast something)."
Allow the paste to cool completely before transferring to an airtight container. The paste will keep in the refrigerator for 3 weeks, or in the freezer for up to 3 months.