Heat the canola oil over medium heat in a large saute pan. Season the pheasant with salt and pepper and coat with the softened butter. Brown all sides of the pheasant until golden brown and remove to a utility platter. To the same pan, add the onion and garlic and saute until the onion becomes translucent. Deglaze the pan with the Marsala wine and add bay leaves and parsley. Lower the heat and return the pheasant to the pan. (Wash and dry the utility platter and keep handy for the cooked pheasant.) Cover and simmer until the pheasant is tender and juices in the thigh run clear when pierced, about 35 minutes. Remove the pheasant to the utility platter and allow to rest until cool enough to handle.
Strain the braising juices into another pot and skin off any excess fat. Add balsamic vinegar and brown sauce and cook over medium heat until thickened.
Pull pheasant meat from the bones and cut into 1-inch pieces, discarding bones. Remove sauce from heat. In a bowl fold pheasant meat with enough sauce to coat. Do not feel obligated to use all of the sauce. The mixture should not be soupy.
Preheat oven to 400 degrees F.
Roll out the pastry dough and, using an appropriately sized cereal bowl or small mixing bowl as a template, cut 4 rounds 8-inches in diameter.
Spoon the pheasant mixture evenly into 4 individual ovenproof 6-inch bowls (onion soup bowls are ideal for this), and brush the edges of the bowls with egg. Top each with a circle of pastry, draping the crust over the rim. Brush the tops of the pastry with the egg wash and bake until golden, about 12 to 15 minutes.
This recipe has been updated and may differ from what was originally published or broadcast.