In a large heavy saucepan, cook the sausage over moderate heat until browned. With a slotted spoon, transfer the sausage to a plate.
Chop the scallions, reserving the dark green parts for garnish; add the white and pale green parts to the saucepan. Add the green pepper, celery, and garlic. Cook over moderate heat, stirring, for 5 minutes. Add the broth, rice, thyme, and reserved sausage. Bring the mixture to a boil. Reduce the heat to a simmer and cook the jambalaya, covered, for 10 minutes. Stir in the shrimp and pepper and cook the mixture, covered, for 10 to 15 minutes more or until the shrimp are just done and the rice is tender.
Serve the jambalaya sprinkled with the reserved scallion greens.
You don't need to add salt, as it is provided by the canned broth and sausage.
Recipe courtesy of Leslie Glover Pendleton, author of Simply Shrimp, Salmon, and (Fish) Steaks