Melt 1/4 cup butter in a Dutch oven.
Peel and devein shrimp, placing shells in the Dutch oven and cook over medium heat until the shells turn pink.
Add the cartons of chicken broth and bring to a boil. Reduce heat to low and continue to simmer 20 minutes. Remove from heat and cool. Strain the broth through fine sieve and set aside for later use. Discard the shells.
Brown the sliced Andouille in a large Dutch oven. Remove from heat and set aside until needed.
Add oil and remaining butter to the Dutch oven. Heat until butter is completely melted. Add flour and stir with a wooden spoon until smooth. Reduce heat to low and continue to cook, stirring frequently, until roux is a dark caramel color. This will take 30-40 minutes. Do not shorten this process! This is key in achieving that dark, savory flavor. Stir frequently toward the end to prevent burning.
In a cast iron skillet, cook the chopped onion in a little oil for five minutes. Add the celery and green pepper and cook another five minutes. Add the garlic and cook 1 minute more.
Add onion mixture to the cooked roux and then the beer, stirring constantly. Add the shrimp/chicken broth in batches.
Add the Cajun seasoning, Worcestershire, thyme, and bay leaves, plus the andouille sausage. Bring to a boil. Reduce heat to medium-low, cover and simmer for 1 1/2 hours
Add green onions, parsley, and shrimp. When shrimp are pink, remove from heat and stir in crabmeat. Serve immediately.
Serve with a dollop of cooked rice.