Place a 9- or 10-inch Dutch oven over medium heat and add the olive oil. When the oil is hot, add the celery, carrots, onion, and garlic. Cook, stirring often, until the vegetables have softened, 8 to 10 minutes.
Season the chicken with salt and pepper. Increase the heat to medium-high, add the chicken, and cook until lightly browned, 5 to 7 minutes. Add the white wine and reduce it slightly, 30 seconds. Stir in all the remaining stew ingredients except the cornstarch. Simmer over low heat, partially covered, until the vegetables are tender, 35 to 40 minutes.
While the stew simmers, prepare the biscuits: In a large bowl, combine the flour, baking powder, baking soda, and salt, and stir with a fork to blend. Add the oil and buttermilk, and mix until the ingredients are just incorporated. Set aside.
Preheat the oven to 375F.
Stir the cornstarch into ½ cup water to form a slurry. Stir this into the simmering stew and cook for 2 to 3 minutes, until thickened.
Drop tablespoons of the biscuit dough over the top of the stew. Transfer the pot to the oven, and bake for 20 minutes. Sprinkle the cheddar over the biscuits, return the pot to the oven, and bake for another 5 minutes, until the cheese is melted and slightly browned. Serve immediately.
Variations:
Add chopped or sliced rutabaga or parsnips with the celery and carrots.
Add peas or chopped cooking greens during the last few minutes of cooking.
Substitute pork or beef for the chicken; the stewing time needed to tenderize may increase, so add about 1 cup extra stock or broth.
Use turkey instead of chicken.
Substitute 1/3 cup whole wheat flour for 1/3 cup of the all-purpose flour.
Make individual pot pies in small casseroles.
Indian: Some curry, turmeric, a pinch of garam masala, and a spoonful of spicy mango chutney will steer you in this direction.
Mexican: Use bell and chile peppers, beans, corn, and chili powder.
Thai: Use red or green curry paste, cilantro, and coconut milk.
