INGREDIENTS
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1 whole chicken (3 1/2 to 4 pounds), cut into 11 pieces (reserve back and wing tips for another use, such as stock)
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Coarse salt and freshly ground pepper
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3 tablespoons unsalted butter, softened, divided
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1 tablespoon extra-virgin olive oil
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1 small yellow onion, cut into 1/4-inch dice (1 cup)
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1 carrot, cut into 1/4-inch dice (1/2 cup)
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1 celery stalk, cut into 1/4-inch dice (1/3 cup)
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8 ounces cremini mushrooms, trimmed and quartered
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2 tablespoons all-purpose flour
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2/3 cup dry white wine
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4 cups chicken broth
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2 sprigs fresh flat-leaf parsley
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2 sprigs fresh thyme
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1 bay leaf
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2 large egg yolks, room temperature
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1/4 cup heavy cream
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2 to 3 tablespoons roughly chopped fresh tarragon leaves
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2 tablespoons fresh lemon juice