1. Bring a small saucepan of water to boil. Add onions and cook 30 seconds; drain. Rinse onions under cold water. Remove a thin slice from the root end of each and slip off outer skins.
2. Combine flour, 1/2 teaspoon salt, 1/2 teaspoon poultry seasoning, and pepper in a large, resealable plastic bag. Add chicken and shake to coat.
3. Heat oil in a large Dutch oven over medium-high heat. Add half of the chicken; reduce heat to medium and cook until chicken is well browned on both sides. Repeat with remaining chicken. Set aside. Add mushrooms to pan and cook 5 minutes, stirring until liquid has evaporated.
4. Add broth, wine, and cream to saucepan with mushrooms (mixture may look curdled). Add onions, chicken, carrot, celery, remaining salt and poultry seasoning; bring to a boil. Reduce heat and simmer, covered, stirring occasionally until chicken is tender, 30 minutes. Sprinkle with herbs just before serving. Makes 4 servings.