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Step 1
Pour the wine into a large saucepan, and warm it over medium heat until it is hot. Carefully set it aflame. Let the flames die out, then bring it to a boil over high heat. Let it continue to boil until it is reduced by half. Remove it from the heat and set aside.
Step 2
Heat the oven to 350 degrees, with a rack in the center of the oven. Season the short ribs all over with salt and the crushed pepper. Warm the oil in a wide Dutch oven over medium-high heat. Dust half the short ribs lightly with flour, and when the oil is hot, place them in the Dutch oven and sear about 4 or 5 minutes on each side, until well browned. Transfer them to a plate and repeat with the othr 4 short ribs.
Step 3
Pour out all but about 1 tablespoon of fat from the Dutch oven, reduce the heat to medium, and add the garlic, shallots, carrots, celery, leek, parsley, thyme and bay leaves. Brown the vegetables lightly, stirring now and then, about 5 to 7 minutes. Stir in the tomato paste and cook for one minute, blending well.
Step 4
Add the reduced wine and browned short ribs, then pour in enough of the broth to just cover the ribs. Bring the liquid to a boil over high heat, cover the Dutch oven tightly and put it into the hot oven to braise for 2 1/2 hours. Every half hour or so, lift the lid and skim the fat off. Add more broth as necessary to keep the short ribs just covered. The ribs are done when they feel very tender when poked with a fork. (At this point, you can let it cool, then chill the ribs in their covered Dutch oven overnight. Remove the fat, rewarm and proceed with recipe.)
Step 5
Taking care so the tender meat does not fall apart, gently transfer the short ribs to a heated serving platter with a rim or a half-sheet pan and keep warm. If the short ribs have bones and they are falling out, you may want to gently remove the bones. Bring the liquid in the Dutch oven to a boil over high heat and let it reduce and thicken until you have about 1 quart (4 cups). Taste the sauce, and adjust seasoning, adding salt and pepper as necessary. Place a fine-mesh strainer over a bowl and pour the sauce through; discard the solids. (At this point, the ribs and sauce can be combined and kept covered in the refrigerator for 2 to 3 days. Reheat gently, basting frequently, on top of the stove or in a 350 degree oven.)
Step 6
To serve with the celery duo, rewarm the celery root purée and glazed celery if necessary. Warm the plates, divide the celery root purée between them. Top each with a short rip, ladle some sauce over it, letting it spill over the sides of the purée. Place a glazed celery quarter on each and garnish with celery leaves, if desired.