Melt the butter in a large, heavy casserole, add the onion, chopped celery, and chopped carrot, and cook the vegetables, stirring occasionally, for 5 minutes. Add the garlic and cook, stirring, 1 minute. Add the wine and reduce 1 minute. Add the chicken stock, rosemary, bay leaf, salt, and pepper, to taste. Add the chicken to the pot and bring liquid to a boil.
Reduce the heat to low, cover and simmer, skimming and stirring occasionally, for about 30 minutes.
Remove the chicken from the pot and transfer to a cutting board. When cool enough to handle, remove meat from bones. Cut chicken into bite-side pieces. Skim surface of cooking liquid and strain it through a sieve into a large saucepan. Add the diced vegetables, bring to a boil and simmer for 5 to 7 minutes, or until vegetables are tender.
In a small bowl, whisk together the cornstarch and the cream. Add the cream mixture to the boiling stock, stirring, and simmer until lightly thickened. Add chicken to saucepan and correct the seasoning adding the lemon juice and salt and pepper to taste. Bring to a simmer and top with the dumplings, spacing them evenly. Cover, reduce heat to moderate and simmer until dumplings are firm to the touch and cooked through, about 20 minutes. Sprinkle with chives or parsley.;
Into a bowl, sift the flour, baking soda, and salt. Add parsley, the pepper, and the butter and blend until mixture resembles coarse meal. Stir in just enough buttermilk to form a soft dough.
Gently pat the dough into a 1/2-inch thickness and stamp or cut into 1 1/2-inch pieces.