Peel and devein shrimp, placing shrimp shells in a large pot. Refrigerate shrimp until needed.
In a large pot, melt 1/4 cup butter over medium heat. Add shrimp shells and cook until pink. Then add broth.
Bring broth to a boil, reduce heat and simmer 15 minutes. Remove from heat and keep warm until needed.
In a large Dutch oven, cook sausage until browned. Remove sausage with a slotted spoon and set aside.
Add oil and remaining 1/4 cup butter to Dutch oven. Heat over medium heat until butter is completely melted.
Add flour and stir with wooden spoon until smooth.
Reduce heat to medium low and cook, stirring frequently until roux is a dark caramel color. This will take 30 to 40 minutes.
Add onion and cook for 5 minutes, stirring frequently.
Add green pepper and celery and cook for 5 more minutes, stirring often.
Add garlic and cook 1 minute.
Add beer and stir in well.
Pour shrimp stock through a fine-meshed sieve into Dutch oven. (I like to add it in 3 separate additions, mixing well between additions.
Add Cajun seasoning, Worcestershire sauce, thyme, and bay leaves, plus the reserved andouille sausage. Bring to a boil. Reduce heat to medium-low, cover and simmer for 1 1/2 hours.