Preheat oven to 375 degrees. Mix miso paste into 1 cup of warm water to form miso sauce, mixing until miso paste is completely dissolved. Mix miso sauce, soy sauce, and sesame oil in a large baking tray, forming the base of the marinade. (Lamb and vegetables will be cooked together in this tray, so make sure you use a tray large enough for everything to lay flat together.) Mince garlic and chop shallot finely, and add to marinade. Mix in black pepper, cumin, cayenne pepper. Soak lamb in marinade. Chop rosemary over the top of lamb chops.
Place whole potatoes in the oven, pre-cooking them for 15 minutes at 375 degrees. Cut each persimmon and each summer squash into 6 pieces. Cut each fig in half. Cut portobella mushroom into thumb-sized pieces. Scrub and trim carrots; leave them whole with the skin on. Soak the vegetables in the marinade and leave in the tray with lamb.
After potatoes have pre-cooked (15 minutes at 375 degrees) transfer them to the tray with lamb and vegetables. Moisten all vegetables and potatoes with marinade and place in preheated oven. Cook for 35-40 minutes at 375 degrees. Moisten vegetables every 10-15 minutes. Serve when carrots are tender.
Some of the fat from the lamb will enrich the marinade during cooking, so for best results use a lamb cut which has a little marbling. Extra-lean lamb is less desirable. The lamb and vegetables are never removed from the marinade until serving, hence the marinade becomes the braising sauce. Braising has a tenderizing effect on the lamb.
It is important to use fresh miso mixed into water, and not to substitute a prepared miso sauce unless absolutely necessary. Prepared miso sauces are often much saltier and less sweet than fresh miso preparations. Fresh miso paste can usually be found in the health foods or organic foods refrigerator section of supermarkets, and it will keep for months in the refrigerator after opening.
The lamb and vegetables require the same cooking time. The potatoes, however, require 15 minutes additional cooking time. Use this time to your advantage to cut the other vegetables or make other preparations. Once the pre-cooked potatoes have rejoined the lamb and vegetables the dish "cooks itself".
Enjoy this dish with a zinfandel.