Heat 1 Tablespoon oil in 5-quart stockpot over medium heat.
Add onion, carrots and celery. Cook, stirring often, until onion is tender, approximately 5 to 7 minutes; remove vegetables with slotted spoon and reserve.
Add remaining oil to the pot. Cook the chicken pieces in oil, one layer at a time, turning once, until golden; remove the browned pieces and reserve.
Pour the broth into stockpot and stir, scraping up any brown bits that stick to the bottom of the pot. Stir in bay leaf, marjoram, cooked vegetables and chicken. Cover and simmer 30-45 minutes, or until chicken is tender.
Remove chicken pieces to a dish and keep warm in a low oven.
For dumplings, in a mixing bowl, stir together flour, baking powder and salt. Cut in butter. Add milk and stir with fork until just moistened. Drop dumplings, one at at time, into simmering stock. Cover and simmer for 8 minutes, or until cooked all the way through.