Melt butter over medium heat in a deep frying pan. Stir in diced ham and cook until lightly browned, about 5 minutes.
Stir in red bell pepper, celery, white portions of green onion, jalapeno pepper, and garlic; cook, stirring, until softened, about 5 minutes. Stir in Cajun seasoning and cook for 1 minute.
Stir in flour; cook and stir until flour is no longer gritty, about 3 minutes. Pour in chicken broth and Worcestershire sauce; increase heat to medium-high. Simmer until vegetables are soft and liquid is reduced and thick, 10 to 15 minutes. Reduce heat to medium-low.
Stir in shrimp; cook and stir until shrimp are cooked through, 2 to 3 minutes. Season with salt and cayenne pepper to taste. Garnish with green parts of green onions.
