Red-Wine-Braised Oxtails

Preheat oven to 325°F.
In a 4- to 6-quart heavy saucepan boil wine until reduced by about half (about 3 1/4 cups). Trim oxtails and pat dry. Season oxtails with salt and pepper. In a deep heavy ovenproof kettle just large enough to hold oxtails in one layer heat 1 tablespoon butter over moderately high heat until foam subsides and brown half of oxtails on all sides, transferring to a bowl. Brown remaining oxtails in 1 tablespoon butter in same manner and transfer to bowl. Coarsely chop shallots, garlic, carrots, leeks, onion, and celery. Add vegetables to kettle and cook in 1 tablespoon butter over moderately low heat, stirring, until softened.
Arrange oxtails over vegetables and add reduced wine, herbs, and enough broth to just cover oxtails. Bring liquid to a boil and braise oxtails, covered, in middle of oven 3 to 3 1/2 hours, or until meat is very tender but not falling off the bone. Transfer oxtails with a slotted spoon to a bowl and keep warm. Pour braising liquid through a fine sieve into a large saucepan and discard solids. Boil liquid until thick, shiny, and reduced to about 1 3/4 cups and whisk in remaining tablespoon butter.
Serve oxtails and sauce with celery root puree or mashed potatoes.