Ingredients:

4 pounds chicken legs, split
Kosher salt
Freshly ground pepper
1/4 cup canola oil
1 medium onion, chopped
1 medium carrot, chopped
1 celery rib, chopped
2 medium shallots, chopped
1 1/2 cups dry Riesling
1 1/2 cups chicken stock
4 thyme sprigs
2 tablespoons unsalted butter
2 tablespoons extra-virgin olive oil
1 pound mixed mushrooms, sliced
1/2 cup crème fraîche
2 teaspoons fresh lemon juice
Finely chopped tarragon, for garnish

How to Make: 

Preheat the oven to 300°. Season the chicken with salt and pepper. In a
large, enameled cast-iron casserole, heat 2 tablespoons of the canola
oil. Add half of the chicken and cook over moderately high heat,
turning, until browned, 8 minutes. Transfer to a plate. Cook the
remaining chicken, then pour off the fat and wipe out the casserole.

Heat the remaining 2 tablespoons of canola oil in the casserole. Add the
 onion, carrot, celery and shallots and cook over moderate heat,
stirring, until the vegetables are softened and lightly browned, 8
minutes. Add the wine and simmer for 1 minute, scraping up the browned
bits from the pot. Add the chicken stock and thyme and bring to a boil.

Nestle the chicken in the casserole; cover and braise in the oven for 1 hour, until tender.

Meanwhile, in a very large skillet, melt the butter in the olive oil.
Add the mushrooms and cook over high heat, without stirring, until well
browned, 5 minutes. Season the mushrooms with salt and pepper and cook,
stirring, until tender, 3 to 5 minutes; transfer to a plate.

Transfer the chicken to a plate. Strain the braising liquid through a
fine sieve into a heatproof bowl, pressing on the solids; skim off the
fat. Return the braising liquid to the casserole and boil until reduced
to 1 1/2 cups, 3 to 5 minutes. Whisk in the crème fraîche and lemon
juice and season with salt and pepper. Add the mushrooms and chicken to
the sauce and simmer for 3 minutes. Garnish with tarragon and serve.

Source  : http://www.foodandwine.com/recipes/coq-au-riesling