Rinse chicken well and pat it thoroughly dry. Heat the butter and oil in a large (at least 8 qt.) 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. Then add the herbs and rutabaga. Cover, and leaving the heat at medium-high, bring to a boil. Cook until rutabaga is nearly soft through but still somewhat crisp, about 10 minutes. Add the potato and the carrots, cover, and cook until carrots are nearly tender, about 15 minutes.
While the stew is cooking, make the dumpling dough. To do this, sift the flour, baking powder, 1 ts. salt, baking soda and nutmeg together into a medium-size bowl. Make a well in the middle and add the egg, 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 or raisins.
Adjust the seasoning of the stew and make sure it is boiling merrily; 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. Check them occasionally to be sure they don't overcook and become dry.
To serve, cut through the dumplings with a serving spoon, and laddle the chicken and vegetables into warmed shallow soup bowls (remove the thyme and bay leaves). Place the dumplings on top, serve immediately.