In a large kettle cook the sausage over moderate heat until lightly browned, and transfer it to a plate.
Chop the scallions, reserving the dark green parts for garnish, and add the white and pale green parts to the kettle. Add the green pepper, celery, and garlic and cook over moderate heat, stirring, for 5 minutes. Add the broth, rice, thyme, sausage and salt and pepper to taste, and bring the mixture to a boil. Reduce the heat to a simmer and cook the jambalaya, covered, for 15 minutes. Add cornstarch and stir until completely blended.
Stir in the shrimp and cook the mixture, covered for 5 to 10 minutes more or until the shrimp are just done. Add hot sauce to taste.
Recipe by Leslie Glover Pendleton