How to Make It
In a large enameled cast-iron casserole, heat the oil until shimmering. Season the chicken with salt and black pepper. Working in batches, brown the chicken over moderately high heat, 5 to 7 minutes. Transfer the chicken to a plate.
Add the onion, carrot and celery to the casserole and cook over moderate heat, stirring occasionally, until lightly browned, 7 to 8 minutes. Add the garlic and mushrooms and cook for 2 minutes. Stir in the tomato paste and cayenne and cook, stirring frequently, until deep mahogany, about 5 minutes. Add the wine, bay leaf and thyme and simmer for 2 minutes. Add the broth and chicken and bring to a boil. Cover and simmer over moderate heat until the chicken is very tender, about 1 hour.
In a medium saucepan, combine the turnips and potato with the rosemary and enough water to cover by 1 inch. Season with salt and bring to a boil. Simmer the vegetables over moderate heat until tender, 20 to 25 minutes. Drain the vegetables and discard the rosemary. Transfer the turnips and potato to a food processor, add the cream and butter and puree until smooth. Season the turnip puree with salt and pepper and keep warm.
Transfer the chicken to a plate. Boil the cooking liquid until thickened and reduced to 21/2 cups, about 10 minutes. Discard the bay leaf and thyme. Coarsely shred the chicken and stir it into the reduced sauce; discard the skin and bones. Simmer gently until the chicken is warmed through, about 2 minutes. Serve the chicken fricassee with the creamy turnips.