1In a large saucepan, combine the first five ingredients. Bring to a boil. Reduce heat, and simmer uncovered for 30 minutes. Strain the broth and set aside. In a dutch oven, saute carrots, celery and onion in oil and butter until tender, and onion almost translucent.
2Add minced garlic; cook 1 minute longer. Stir in flower until blended, and begin gradually adding prepared broth-1 cup at a time. Bring to boil, cook about 2 minutes until thickened; stirring after each addition.
3Add peas, and return to a boil. Cook 3-5 minutes until peas are tender. Stir in chicken and cream; heat through.
Combine flour, baking powder, salt, cayenne and chive seasoning in large bowl. In a separate bowl, combine buttermilk and eggs. Stir into dry ingredients just until moistened
5Drop dumpling mixture by tablespoonfuls onto simmering chicken mixture. Cover and simmer (do not lift cover while simmering) 15-20 minutes longer, or until toothpick inserted in a dumpling comes out clean. Garnish with minced chives.