Rinse chiles and slice them open so they'll lay flat, discarding stems, seeds, and ribs.
Bring the pork broth to boil (reserving the garlic and onions from the broth).
Heat a cast-iron skillet over medium heat, and toast the chiles in batches, skin sides up for about 30 seconds (be careful not to burn them).
Transfer the toasted chiles to a heat proof bowl and pour boiling pork broth over them.
Soak chiles, stirring occasionally, about 15 minutes, or until softened.
In a food processor, purée the chiles with 3 cups of the soaking broth until smooth (reserving the rest of the soaking broth).
Pour the puréed chiles through a sieve into a bowl, pressing on solids, and discard solids.
Stir the reserved soaking broth into chile mixture.
Cook the garlic, cumin, and oregano in oil in a large heavy saucepan over medium low heat, stirring, 2 minutes. Add the reserved onions and garlic from the broth and stir to combine.
Add the masa harina or corn starch and cook, stirring, 2 minutes.
Add the chile mixture, stirring to combine. Simmer, partly covered, stirring occasionally, about 30 minutes.
Season with salt, vinegar, and sugar and stir to combine.
Mix 1-1½ cups of the sauce with the shredded pork. Reserve the rest to serve on top of the tamales.
This nutritional information has been automatically calculated, and as such, may be incomplete or inaccurate. Please reference the specific ingredients you use for the most accurate nutritional information.