1Heat oven to 350°. Cut each pheasant in half along backbone and breastbone from tail to neck with kitchen scissors. Mix flour, seasoned salt and pepper in shallow bowl. Coat pheasant generously with flour mixture. Reserve remaining flour mixture.
2Heat oil in 12-inch skillet over medium-high heat. Cook pheasants in oil 3 to 4 minutes on each side or until well browned. Place in ungreased rectangular pan, 13x 9 x 2 inches, or in shallow roasting pan. Top and surround pheasants with mushrooms and carrots.
3Melt butter in 2-quart saucepan over medium heat. Add enough additional flour to remaining flour mixture to make 2 tablespoons. Stir flour mixture into butter. Cook, stirring constantly, until mixture is smooth and bubbly; remove from heat. Gradually stir in half-and-half and broth. Heat to boiling, stirring constantly. Boil and stir 1 minute. Stir in sherry and oregano. Pour evenly over pheasants.
4Bake uncovered 1 hour 15 minutes to 1 hour 30 minutes, spooning sauce in pan over pheasants once, until pheasants are tender and juice is no longer pink when centers of thickest pieces are cut. Remove pheasants from pan with slotted spoon. Stir sauce until smooth. Serve sauce with pheasants.