Place 1/2 cup broth in a medium saucepan over low heat; add flour, and stir until smooth. Cook 1 minute, stirring constantly. Gradually add remaining 1/2 cup broth; cook over medium heat, stirring constantly, until thickened and bubbly. Set aside.
Sauté mushrooms in butter in a small skillet 3 to 5 minutes. Stir mushrooms, chicken, and seasonings into white sauce.
To serve, slice individual cornbread squares in half horizontally; spoon chicken mixture over the bottom half of each square. Replace top half of each square, and spoon about 1 tablespoon of chicken mixture over top.