Melt 2 tablespoons butter in a large heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add broth; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Stir in seasonings. Set aside.
Sauté mushrooms in 1 1/2 teaspoons butter in a small skillet; stir into white sauce. Stir in turkey, pimiento, and chopped parsley, mixing well. Spoon hash over Cornmeal Patty Cakes or hot cooked rice. Garnish with fresh parsley sprigs, and serve immediately.