Toast the dried chiles in a Dutch oven over medium-high heat, stirring frequently, until slightly darkened, with an intense roasted aroma, 2 to 5 minutes; turn down the heat if they begin to smoke. Add the chicken stock and simmer until the chiles have softened, 5 to 8 minutes.
Transfer the chiles and liquid to a blender and blend, starting on low speed and gradually increasing the speed to high and scraping down the sides as necessary, until a completely smooth puree if formed, about 2 minutes; add water if necessary if the mixture is too thick to blend. Let cool.
Freeze the chile paste in ice cube trays, putting 2 tablespoons into each well. Once the cubes are frozen, transfer to a zipper-lock freezer bag and store in the freezer for up to 1 year.