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1
Rinse rabbit pieces and remove any fat, then pat dry and divide into 3 batches. Mix together salt and pepper in a small bowl for seasoning rabbit.
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2
Put oven rack in middle position and preheat oven to 350u00b0F.
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3
Heat a dry 12-inch heavy skillet over moderately high heat until hot. Season first batch of rabbit, then add 3 tablespoons oil to skillet and brown rabbit on all sides, about 5 minutes total. Transfer browned rabbit to a flameproof roasting pan just large enough to hold all 3 batches in 1 layer. Season and brown remaining 2 batches of rabbit in same manner, transferring to roasting pan and adding more oil to skillet between batches if necessary. Reserve skillet.
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4
Add broth to roasting pan, then cover pan tightly with foil and braise rabbit in oven 15 minutes.
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5
While rabbit is braising, pour off any fat from skillet, then add onions, garlic, thyme, and 3 tablespoons butter and cook over moderately low heat, stirring and scraping up any brown bits, until onions are softened, about 5 minutes. Add wine and boil until liquid is reduced by half, about 10 minutes.
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6
Pour mixture over rabbit and continue to braise, covered tightly, until rabbit is tender when pierced with a fork, 45 minutes to 1 hour more. Transfer rabbit to an ovenproof serving dish and keep warm, covered loosely with foil, in turned-off oven.
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7
Straddle roasting pan over 2 burners and boil braising liquid until reduced to about 3 1/4 cups, about 10 minutes. Transfer 1/2 cup reduced liquid to a bowl and whisk in mustards. Add mustard mixture to reduced liquid in pan, whisking to incorporate. Dissolve cornstarch in water and whisk into sauce, then simmer, whisking, 2 minutes. Add remaining 3 tablespoons butter to sauce and swirl pan until incorporated. Season sauce with salt and pepper and pour over rabbit.
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8
*Available at butcher shops, specialty foods shops, and some supermarkets (may require special order).
