Remove the stems and tops from the chiles. Either lightly wipe them with a slightly dampened cloth (as is done in Veracruz) or rinse them under cold running water and let them thoroughly dry at least overnight, to be sure no water clings to them.
In a medium-sized heavy-bottomed skillet, heat the oils over a medium heat. When fragrant, add the chiles. Reduce the heat to the lowest possible setting. Cook, stirring constantly, until they are puffed and somewhat red. Be careful not to let them scorch.
Transfer the fried chiles to a medium-sized bowl, reserving the oil left in the skillet. Cover them with boiling water, let stand for 40 minutes, and drain. Reserve a little of the soaking water (¼-⅓ cup) if desired, to help in processing.
Purée the garlic and salt together in a food processor. Add the drained chiles and reserved oil; process until smooth, adding a little of the soaking liquid or more oil if necessary to help the action of the blades. Scrape the paste out into a small container and store in the refrigerator, tightly sealed, for up to a month.