Coq au Riesling

Name: Coq au Riesling
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