Place a large pot on stove over medium high heat. Add oil, butter, vegetables and bay leaf and cook 5 minutes, stirring frequently. Season mixture with salt, pepper and poultry seasoning. Add flour to the pan and cook 2 minutes. Stir broth or stock to the pot and bring to a boil. Add chicken to the broth and stir.
Place biscuit mix in a bowl. Combine with 1/2 cup warm water and parsley. Drop tablespoonfuls of prepared mix into the pot, spacing dumplings evenly. Cover pot tightly and reduce heat to medium low. Steam dumplings 8 to 10 minutes. Remove cover and stir chicken and dumplings to thicken sauce a bit.
Stir peas into the pan, remove chicken and dumplings from heat and serve in shallow bowls.