Place the flour with the coriander, cumin, garlic powder and ground mustard in a shallow dish, and mix well with a wooden spoon. Generously sprinkle the short ribs with salt and pepper, then dredge both sides in the seasoned flour one by one, making sure to shake off any excess flour.
In a large Dutch oven over medium heat, add 2 tablespoons oil. When the oil smokes, add the short ribs in batches. Brown the short ribs until a golden crust starts to form, about 5 minutes on each side. Once brown, reserve and continue until all the ribs are brown, adding more oil as needed. Set the ribs aside.
While the short ribs are browning, heat a cast-iron skillet over medium-high heat. When the skillet is hot, add the pasilla chiles and toast until they start to smoke, about 4 minutes. Remove the chiles and submerge in the hot water. Allow to steep until they become soft and pliable, about 10 minutes. Remove from the water and puree in a blender with 1/4 cup of the steeping water. Set aside the puree.
Preheat the oven to 350 degrees F.
Add the carrots, garlic, onions and celery to the Dutch oven. Cook until the vegetables caramelize, about 15 minutes. Deglaze the pot with the red wine, and then add the tomatoes, beef broth, hominy and reserved pasilla chile puree. Bring the whole mixture to a simmer. Start adding all the browned short ribs back into the pan. Cover and cook until the short ribs barely start falling off the bone, about 1 hour 30 minutes.
Season with salt, pepper, cilantro and parsley; garnish with a lime wedge and serve.
This recipe has been updated and may differ from what was originally published or broadcast.