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1
Preheat oven to 200F.
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2
Pat chicken dry and season with salt and pepper.
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3
Heat butter and oil in a 12-inch deep heavy skillet over moderately high heat until foam subsides, then brown chicken well, about 8 minutes total.
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4
Arrange skin-sides up, then sprinkle with shallot.
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5
Add wine and bring to a boil.
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6
Reduce heat and simmer, covered, until chicken is just cooked through, 20 to 25 minutes.
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7
Transfer chicken with tongs to a heatproof platter, reserving juices in skillet.
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8
Cover chicken with foil and keep warm in oven.
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9
Sift together flour, cornmeal, baking powder and soda, salt, and pepper into a bowl.
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10
Blend in butter with a pastry blender or your fingertips until mixture resembles coarse meal.
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11
Stir in 2 tablespoons chives and 1 tablespoon parsley, then add buttermilk, stirring just until dough is moistened (do not overmix).
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12
Skim fat from juices in skillet.
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13
Add 2 3/4 cups stock and bring to a boil.
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14
Whisk together cream, flour, and remaining 1/4 cup stock in a small bowl until smooth, then whisk into boiling stock and season with salt and pepper.
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15
Drop 8 heaping tablespoons of dough into simmering gravy, about 2 inches apart to allow dumplings to expand.
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16
Reduce heat and gently simmer dumplings, covered, until tops are dry to the touch, 15 to 20 minutes.
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17
Sprinkle chicken, dumplings, and gravy with remaining herbs.
