1Blend flour, 1/2 teaspoon thyme and allspice in small bowl. Set aside 1 tablespoon of flour mixture. Sprinkle chicken with salt and pepper, then with enough of remaining flour mixture to coat.
2Melt butter in heavy large skillet over medium-high heat. Add chicken to skillet. Saute until brown, about 4 minutes per side.
3Transfer chicken to plate. Add mushrooms, onion, and remaining 1 teaspoon thyme to skillet. Saute until mushrooms are brown, about 5 minutes.
4Mix in reserved 1 tablespoon flour mixture; cook 1 minute. Add cream and broth and bring to boil, stirring occasionally. Return chicken and any collected juices to skillet. Reduce heat to medium-low; simmer uncovered until chicken is cooked through and gravy thickens slightly, about 5 minutes. Season with salt and pepper.