Heat a large skillet over medium heat. Add the butter and onion and cook, occasionally stirring, for 3 to 4 minutes, until the onion is softened.
Add the garlic and cook, stirring constantly, for one minute until fragrant.
Add the flour and cook for one minute while stirring constantly.
Slowly include the chicken broth, stirring constantly to prevent lumps.
Add Worcestershire sauce, paprika, cayenne pepper, thyme, as well as a pinch of salt and pepper.
Bring the mixture to a simmer and cook for ten minutes, stirring occasionally, until the mixture has thickened.
Add the shrimp and cook for 4-5 minutes, stirring occasionally, until they are completely cooked.
If necessary, adjust the seasoning to taste.
The Etouffee should be garnished with green onions.