In a large heavy-bottomed pot or Dutch oven, combine the vegetable oil and all-purpose flour over medium heat. Stir continuously for 30-40 minutes until the roux turns a dark chocolate brown color.
Add the chopped onion, green bell pepper, and celery to the dark roux. Stir and cook for 5 minutes until the vegetables soften.
Stir in the minced garlic and sliced beef andouille sausage, cooking for another 3 minutes until the sausage begins to brown.
Gradually pour in the stock while stirring constantly to prevent lumps. Add the Cajun seasoning, dried thyme, and bay leaves. Bring the mixture to a boil, then reduce heat, cover, and simmer for 45 minutes.
Add the peeled and deveined shrimp to the pot and simmer for 5-7 minutes until the shrimp turn pink and opaque.
Remove the bay leaves, garnish with chopped green onions, and serve hot over cooked white rice.