Rinse the chicken and pat it dry. Place the chicken, bay leaf, salt, and 2 cups of water in a 4-quart Dutch oven. Bring to a boil, then reduce the heat to low. Cover and simmer for 1 hour, or until the chicken is tender. Remove the chicken and set aside until it is cool to the touch. Strain the broth, discard the bay leaf, and return the liquid to the Dutch oven. Add the carrots and onions and cook, covered, for 15 minutes.
Meanwhile, remove the skin and debone the chicken. Discard the skin and bones. Cut the meat into large chunks and set aside. When the carrots and onions are tender, drain them, reserving the broth. Leave the vegetables in the Dutch oven and set aside. Add enough water to the broth to measure a total of 2-½ cups of liquid and return it to the Dutch oven. Stir in the peas, mushrooms, seasonings, and chicken. Combine the flour and milk in a small bowl and mix until smooth. Stir the flour mixture into the broth and cook over medium heat, stirring constantly, until it boils and thickens. Pour the hot mixture into a 2-quart casserole.
Preheat the oven to 400°F. Roll out the pastry to fit the top of the casserole. Place the crust over the chicken mixture and trim the edge, leaving enough to form a ridge. Flute the edge and brush with egg wash. Make slits in the top to vent. Bake for 30 to 35 minutes, or until the crust is golden and the filling is bubbly.