*available at specialty produce markets and many supermarkets
** available by request from butchers
Into a bowl of water, squeeze juice from 2 lemon quarters, dropping squeezed quarters into water. Break off and discard stem from 1 artichoke. Bend back outer leaves until they snap off close to base and remove several more layers of leaves until pale inner leaves are reached. Trim base and sides of artichoke with a very sharp stainless steel knife and cut off the top 1 1/2 inches.. Cut artichoke into quarters and cut away choke and spiky purple-tipped leaves. Rub artichoke quarters all over with a remaining lemon quarter and drop it in the bowl of water. Prepare other 3 artichokes in the same manner, using other lemon quarter if necessary.
Preheat oven to 475*F
In a saucepan of boiling salted water, blanch artichokes 3 minutes and with a slotted spoon transfer to a bowl. In boiling salted water blanch Jerusalem artichoke 5 minutes, and drain.
In a flameproof roasting pan, 17 by 11 1/2 by 2 inches, toss artichokes, Jerusalem artichokes, onions, and garlic cloves with 2 Tbsp. Olive oil and salt and pepper to taste. Roast vegetables in middle of oven 20 minutes.
While vegetables are roasting, heat a heavy 12-inch skillet over moderatly-high heat until hot. While skillet is heating, season lamb racks with salt and pepper. Add vegetable oil to skillet and brown lamb, meaty sides down, 2 minutes. Turn lamb over, and brown 2 minutes more. Transfer lamb to a plate and cool slightly.
In a small bowl, stir together chopped garlic, oregano, coarse salt, freshly ground pepper. And remaining 2 tsp. Olive oil, and rub all over lamb
Remove pan from oven and stir vegetables. Arrange lamb over vegetables, rib sides down, and roast 20 minutes. Or until a meat thermometer inserted in fleshy section registers 130*F for medium-rare.
Remove 8 garlic cloves from pan and squeeze garlic out of skins into a blender. Add broth and blend until smooth. Transfer remaining vegetables and lamb to a heated platter, reserving juices in pan, and let rest, covered loosely for 10 minutes.
To pan, add garlic broth and salt and pepper to taste, and on top of stove deglaze over moderately-high heat, scraping up brown bits. Boil sauce until it thickens slightly and transfer to sauceboat.
Cut lamb racks in half or into individual chops and serve with vegetables.
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