1. Break the ancho and pasilla chilies into small pieces and soak in the hot water until softened, about 10 minutes. Remove the chilies and finely chop them. Set aside the chilies and the soaking liquid separately. 

2. Meanwhile, preheat the oven to 375F and put the rack in the middle position. Season the lamb chops with salt and pepper.

3. Heat the olive oil in a large, oven-safe sauté pan over medium-high heat. When the oil is hot and shimmering, add the chops and press them down with tongs to make sure the whole chop makes contact with the pan. Leave them alone to develop a very brown crust, 2-4 minutes. Turn them over, press again, and leave them to brown for a minute on the second side. 

4. Put the pan in the oven and cook the lamb until it reaches an internal temperature of 140F in the thickest part, 8-12 minutes. Remove the chops from the pan and let them rest, loosely covered with foil, for at least 5 minutes.

5. While the lamb is in the oven, sauté the onion and fennel in the olive oil in a medium saucepan until softened. Add the cumin, aniseed, oregano and garlic and cook for another minute. Add the tomatoes, sugar, vinegar, chili soaking liquid, and chicken broth. Bring to a boil and adjust the seasoning with salt. Stir in tomato puree, ketchup, and cider vinegar. Return to a boil and then reduce heat to low and simmer until thickened.

6. Meanwhile, remove the bones and most of the fat from the lamb chops. You should have about 3/4 pounds of meat. Finely chop any large pieces. Add the meat to the simmering sauce and toss to coat.  Continue to simmer until thickened.

7. Warm the pitas in the oven or microwave. Open a pocket in each pita, fill with a portion of the lamb mixture.