Pat chicken pieces dry with paper towels. In a bowl, combine flour, 1 T salt and 1 t pepper. Place oil and butter in a large skillet with high sides or a saucepan; set over med-high heat. Dredge chicken in flour mixture and shake off excess.
Add chicken to pan and brown approx. 5 min per side; add celery, onion, bell pepper and fennel; cook for 2 min. Add thyme, parsley and chicken broth, scraping the pan to release the browned bits from the bottom.
Season with 1 t salt and ½ t pepper and bring to a boil. Reduce to simmer, cover pan and cook for 10 min. Stir in cream and bring back to a simmer. Prepare the dumplings and add as follows:
In a bowl, combine flour, baking powder, salt and herbs. Gradually add milk, gently stirring until flour is moist and a thick batter has formed. Do not over work.
Drop the batter into the simmering chicken mixture, one heaping tablespoon at a time, leaving space between each dumpling. Cover skillet and simmer 20 min. Do not release steam until dumplings are thoroughly cooked. Remove from heat, add seasonings to taste. Gently stir in lemon zest. Serve hot, garnished with fennel fronds and parsley.