In a large, heavy-bottomed pot over medium heat, add a drizzle of olive oil, then add in the sausage, onion, celery, green pepper, and garlic. Stir together and sauté over medium heat until the onions are translucent, about 5 minutes.
Remove the vegetables from the pot and set aside. Add the butter to the pot, let it melt over low heat, then sprinkle in the flour to make the roux. Continue to cook the flour over low heat, stirring constantly until it turns a caramel color and has a smooth texture, about 20 minutes.
Add the vegetables back into the pot, along with the Creole seasoning, bay leaves, tomatoes, and chicken stock. Stir together and cover. Let the pot simmer over low heat for 25 minutes. Stir the stew occasionally to make sure it doesn’t stick to the bottom.
Remove the bay leaves and add in the shredded turkey. Stir to combine, and let it cook for another 5 minutes, just to heat up the turkey.
Sprinkle the green onions over the gumbo and serve.