Remove the stems (and seeds, if you prefer less heat) from the guajillo, ancho, and pasilla chiles. Place the chiles in the hot pork broth. Let them soak for about 10 minutes, or until softened.
Combine the soaked chiles, 1 cup of their soaking pork liquid (strained), 1 cup chicken stock, garlic, onion, Chimayo chili powder, cumin, and Mexican oregano in a blender. Blend until smooth. Reserve 1 cup of salsa roja and set aside (for the masa).
Heat vegetable oil in the pot over medium heat. Once hot, add the rest of the salsa, stirring. Add in the shredded pork. Bring to a simmer, lower heat, and simmer for 20 minutes. Remove and cool.