Chicken with Rosemary Dumplings

2 tablespoons vegetable oil
6 large bone-in chicken-breast halves (31â„4 pounds), skin removed
4 large carrots, peeled and cut into 1-inch pieces
2 large stalks celery, cut into 1â„4-inch-thick slices
1 medium onion, finely chopped
1 cup plus 2 tablespoons all-purpose flour
2 teaspoons baking powder
11â„2 teaspoons chopped fresh rosemary or 1â„2 teaspoon dried rosemary, crumbled
1 teaspoon salt
1 large egg
11â„2 cups milk
2 cups water
1 can (141â„2 ounces) low-sodium chicken broth or 13â„4 cups
Chicken Broth
1â„4 teaspoon ground black pepper
1 package (10 ounces) frozen peas

In 8-quart Dutch oven, heat 1 tablespoon oil over medium-high heat until very hot. Add 3 chicken-breast halves; cook until golden brown, about 5 minutes per side. With slotted spoon, transfer chicken pieces to bowl as they are browned. Repeat with remaining chicken.
Add remaining 1 tablespoon oil to drippings in Dutch oven. Add carrots, celery, and onion and cook, stirring frequently, until vegetables are golden brown and tender, about 10 minutes.
Meanwhile, prepare dumplings: In small bowl, combine 1 cup flour, baking powder, rosemary, and 1â„2 teaspoon salt. In cup, with fork, beat egg with 1â„2 cup milk. Stir egg mixture into flour mixture until just blended.
Return chicken to Dutch oven; add water, broth, pepper, and remaining 1â„2 teaspoon salt. Heat to boiling over high heat. Drop dumpling mixture by rounded tablespoons on top of chicken and vegetables to make 12 dumplings. Reduce heat; cover and simmer 15 minutes.
With slotted spoon, transfer dumplings, chicken, and vegetables to serving bowl; keep warm. Reserve broth in Dutch oven.
In cup, blend remaining 2 tablespoons flour with remaining 1 cup milk until smooth; stir into broth mixture. Heat to boiling over high heat; boil 1 minute to thicken slightly. Add peas and heat through. Pour sauce over chicken and dumplings.