Melt 1 tablespoon butter in a Dutch oven over medium heat.
Add onion, bell pepper, celery, and garlic to pan; cook 8 minutes or until very tender and onion begins to brown, stirring frequently.
Place onion mixture in a bowl. Melt remaining 3 tablespoons butter in pan. Stir in flour; cook 6 minutes or until flour turns a deep rust color, stirring constantly. Stir in Cajun seasoning, thyme, and clam juice; cook for 1 minute. Stir in onion mixture, tomato, and Worcestershire sauce; simmer for 15 minutes or until thick.
Add green onions, salt, and shrimp; cook for 6 minutes or until shrimp are done, stirring occasionally.