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1
Preheat the oven to 325.
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2
In a large enameled cast-iron casserole, heat the vegetable oil.
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3
Season the ribs with salt and pepper and cook over moderately high heat, turning a few times, until richly browned, about 10 minutes.
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4
Transfer the ribs to a plate.
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5
Add the sherry to the casserole and boil, stirring to scrape up the browned bits on the bottom.
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6
Add the soy sauce, mirin, onion, garlic, ginger, shiitake, brown sugar and half each of the daikon and the carrots.
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7
Return the ribs to the casserole and pour in the water.
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8
Bring to a boil.
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9
Cover and braise in the oven for about 2 1/2 hours, until the meat is very tender.
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10
Transfer the ribs to a plate; cover and keep warm.
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11
Pick out the shiitake mushrooms, cutting off and discarding the stems.
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12
Strain the braising liquid.
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13
Return the liquid to the casserole and boil over high heat, skimming any fat from the surface, until reduced to 4 cups, about 5 minutes.
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14
Add the remaining daikon and carrots to the casserole along with the sesame oil and shiitake mushrooms.
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15
Cover and simmer over low heat until the vegetables are tender, 20 minutes.
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16
Return the ribs to the casserole and simmer until heated through.
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17
Season with salt and pepper.
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18
Meanwhile, bring a saucepan of water to a boil.
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19
In a bowl, cover the noodles with warm water; let stand until pliable, 5 minutes.
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20
Drain the noodles and cut into 4-inch lengths.
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21
Add the noodles to the saucepan and cook until tender but still chewy, 25 seconds.
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22
Drain and transfer the noodles to shallow bowls.
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23
Nestle the ribs on the noodles, ladle the vegetables and broth on top and serve.
