Heat a large skillet over medium-high heat. Add the ancho and pasilla chiles and press them flat with a spatula. Toast the chiles, turning them over, until they're fragrant and their color changes slightly, about 30 seconds. Remove the chiles from the skillet and put them in a bowl. Cover with about 4 cups of boiling water. Weight them with a plate to keep them submerged, if necessary, and soak until tender, about 30 minutes.
Toast the spices and oregano
Meanwhile, heat a small, heavy skillet over medium-high heat. Add the cumin and coriander and toast, giving the pan an occasional shake, until the seeds are fragrant, about 5 minutes. Grind the seeds in a spice grinder or crush them in a mortar and pestle. In the same hot pan, toast the fresh oregano (don't toast dried oregano). Remove the leaves after they've begun to dry out but before they lose all of their green color, about 3 minutes. Set aside.
Reserve 1 cup of the liquid from the soaking chiles and then drain them. Put the chiles and the reserved liquid in a blender. Add the toasted, ground cumin and coriander, the toasted (or dried) oregano, the tomatoes, garlic, and onion. Purée until smooth.
Cut the pork into 1/2-inch cubes, pat it dry, and season it lightly with coarse salt.
In a large, heavy-based skillet, heat 2 Tbs. of the oil until very hot. Brown the pork in the oil in batches (adding more oil to the pan as needed), being careful not to overload the skillet or the pork will stew in its own juices and not brown. Transfer the browned pork to a plate lined with paper towels. Drain off any excess fat from the skillet but leave a light coating on the bottom and don't clean the skillet.
To the hot skillet, add the chile purée carefully; it will splatter while it sizzles. Bring to a boil, stirring constantly. Add the browned pork, reduce the heat to a simmer, and cook, stirring occasionally, until the meat is very tender, about 1-1/2 hours. Add a little water to the pan if the sauce seems too thick. Season with salt to taste and serve.
Serve with warm tortillas, chopped white onions, sprigs of cilantro, slices of avocado, and grated Cotija or aged Cheddar cheese.