In a large stock pot or Dutch oven over medium high heat, add the oil. Add the onions and carrots and saute for 1 minute. Add the chicken and cook just until the chicken starts to brown, but is not cooked through. Add the mushrooms, peas, and 1/4 teaspoon salt and stir to combine. Add the chicken broth and set pan over high heat. Bring to a boil. Let simmer 10 minutes.
Meanwhile, in a medium bowl, combine flour, baking powder, baking soda, parsley, 1/4 teaspoon salt and pepper. Add buttermilk and oil and stir with a fork until mixture comes together. Using a large spoon or a small ice cream scoop, drop 8 golf ball size (mold with your hands, if necessary) dumplings into simmering liquid. Cover pan and cook 5 minutes (no peeking!), until dumplings are puffed up and cooked through.