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.