Cut chicken into 11/2-inch pieces. In a bowl, mix together 3 tablespoons flour and salt and pepper to taste. Add chicken and toss until pieces are evenly coated.
In a 12-inch nonstick frying pan, melt half the butter over medium high heat. Add chicken and cook, turning once or twice, until pieces are lightly browned but chicken is still pink in center (cut to test), about 3 minutes.
With tongs, transfer chicken to a platter and set aside. Melt remaining butter in pan. Add mushrooms, thyme, and garlic. Stir, then cover pan and let cook until mushrooms exude juices, 4-5 minutes.
Remove cover and cook, stirring often, until mushrooms are well browned and pan juices have evaporated, about 2 more minutes.
Sprinkle remaining flour over mushrooms and stir over heat 1 minute.
Add chicken, broth and cream to pan. Cook, stirring often, until sauce has thickened and chicken is no longer pink in center (cut to test), 2-3 minutes.
Transfer fricassee to a serving bowl and serve over egg noodles if desired.
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