In a large skillet, melt butter over medium heat. Stir in flour and cook, stirring constantly, until the roux turns a deep golden brown (about 10 minutes).
Add the onion, bell pepper, and celery. Cook for 5 minutes until softened. Stir in garlic and cook for another minute.
Slowly whisk in the broth, making sure there are no lumps. Add diced tomatoes, paprika, cayenne, thyme, black pepper, salt, bay leaf, and Worcestershire sauce. Stir well.
Reduce heat and let simmer for 20 minutes, stirring occasionally.
Add the shrimp and cook for 5 minutes until they turn pink and opaque. Remove bay leaf.
Stir in green onions and parsley. Serve hot over cooked white rice.
Notes
For a spicier étouffée, increase the cayenne pepper or add hot sauce to taste.