Cut your chicken into 8 pieces. 2 breast halves with ribs and back portion, 2 wings, 2 thighs with back portion and 2 drumsticks. Rinse chicken well and pat it thoroughly dry.
Heat 2 tablespoons butter and oil in 8 quart heavy stockpot or Dutch oven over medium-high heat. When it is hot, add the chicken pieces, season them generously with salt and pepper, and brown on both sides, seasoning the other side when you turn the pieces. Brown the chicken in several batches to avoid crowding the pan, 8 minutes per batch.
Transfer chicken to a plate or bowl, drain off half the fat in the pan, and then return the chicken to the pan. Add enough water to just cover the chicken. Add bay leaves, thyme, allspice berries and rutabaga. Cover, and leaving the heat at medium-high, bring to a boil. Cook until rutabaga is nearly fork tender, about 10 minutes. Add potatoes and carrots, cover, and cook until carrots are nearly tender, about 15 minutes.
While the stew is cooking, make the dumpling dough. Sift the flour, baking powder, 1 teaspoon salt, baking soda and nutmeg together into a medium-size bowl. Make a well in the middle and add the egg, 2 tablespoons melted butter and buttermilk; mix them together in the well with a small whisk, a fork or your fingers. Working quickly, incorporate the dry ingredients to make a fairly stiff dough. Fold in the blueberries.
Taste and adjust the seasoning of the stew and make sure it is boiling; then stir in the peas and parsnips. Next, one heaping tablespoon at a time, drop the dumpling dough on top of the stew so the dumplings are not touching. Cover, and cook just until the dumplings are puffed and cooked through, no longer than 15 minutes.
To serve, cut through the dumplings with a serving spoon. Ladle the chicken and vegetables into warmed shallow soup bowls, remove the thyme sprigs and bay leaves. Place the dumplings on top; serve immediately.