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This recipe was uploaded by Kye
Heat one and one-half tablespoons of the butter and the oil in a heavy skillet, and add the chicken pieces skin-side-down. Cook until nicely browned, about two minutes. Turn and cook on the second side about three minutes or until nicely browned.
Remove the chicken pieces. Pour off the fat and add the remaining butter to the skillet. Add the shallots, carrots, onion and garlic. Cook over low heat, stirring, about 10 minutes.
Add the Cognac and wine and bring to the boil, stirring to dissolve the brown particles that cling to the bottom and sides of the pan. Add the tomato paste, saffron, salt and pepper, and stir. Cover closely and cook over very low heat 30 minutes.
Meanwhile, put the crawfish or shrimp in a saucepan and add cold water to cover. Add salt, pepper, bay leaf and thyme. Bring to the boil and let simmer two minutes. Let stand briefly.
The crawfish or shrimp can be peeled before hand. Set aside.
When the chicken is ready, add the cream, tarragon and cayenne, and stir. Add the crawfish or shrimp, bring to the boil and heat thoroughly. Serve with rice.