Cube the chicken in 1-2 inch sized pieces, season with salt and pepper to taste. Coat the pieces in flour, shaking off the excess and reserving remaining flour. Put oil in skillet and heat over medium-high heat. Add the chicken and brown all sides, about 5 minutes per side. Remove the chicken to a bowl then add carrots, celery, onion, mushrooms. Sprinkle with remaining flour and give it a good stir. Add chicken broth and stir. Nestle the chicken pieces into the vegetables and add enough water to just cover the chicken. Bring to a boil, reduce heat, cover and let simmer for 20 minutes. Just before the cooking time is up combine the baking mix, poultry season and milk in a small bowl. Drop the batter by tablespoons on top of the simmering chicken leaving some room between the dumplings. Cover and simmer for 20 minutes. Serve hot.
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