Combine the onion, celery, carrots, potatoes, garlic, broth, salt and pepper and squirrel (or chicken) in a large pot and bring to a boil; simmer until meat is very tender and easily removed from bones. Debone the meat and set aside; reserve 2 1/2 to 3 cups cooking liquid.
Fit the bottom crusts into 2 pie pans. (The box of Pillsbury refrigerated pie crusts said to lightly brown the bottom crust before filling with pot pie mixture.).
Combine the meat, vegetables, reserved broth and cornstarch in a large bowl and mix well; divide the mixture between the 2 pie shells. Top with the second crust, press the edges to seal and cut vents in the top for steam to escape.
Bake at 350 degrees until crust is browned, about 1 hour.