Chicken Stew with Parsley Dumplings

Name: Chicken Stew with Parsley Dumplings
Ingredients: 1 teaspoon vegetable or olive oil; 2 cups chopped onions; 1 cup sliced carrots; 1 pound boneless, skinless chicken breast, cut into bite-size pieces, about 2 cups; 2 cups sliced mushrooms; 1 cup frozen peas; 1/2 teaspoon salt, divided; 8 cups reduced-sodium chicken broth; 1 cup all-purpose flour; 1 1/2 teaspoons baking powder; 1/2 teaspoon baking soda; 2 tablespoons chopped fresh parsley leaves; 1/4 teaspoon pepper; 1/2 cup buttermilk; 1 tablespoon olive oil