In a large pot or Dutch oven, melt 1 tablespoon of butter over medium heat.
Add the Andouille sausage into the pot and cook, stirring occasionally, for about 6 minutes or until lightly browned. Transfer the sausage to a plate lined with paper towels to drain, reserving the drippings in the pot or Dutch oven.
Add the remaining butter to the pot. Gradually whisk in the flour; and cook, whisking constantly, until the flour is a deep milk chocolate brown color, about 8-10 minutes (it can take longer if you are carefully cooking the roux over low heat). Be vigilant about stirring and paying attention to what is going on in the pot. If at any point you feel the roux is browning too fast, turn the heat down to low.
Add the onions, celery, bell pepper, garlic, Worcestershire sauce, salt and pepper; cook, stirring often, until the vegetables are tender, about 6-8 minutes.
Gradually add the stock, stirring until combined. Add the tomatoes, oregano, thyme, and bay leaves. Bring to a boil over medium-high heat; reduce the heat to low, and simmer, stirring occasionally for about 20-25 minutes or until slightly thickened.
Return the Andouille sausage to the pot, cover and simmer, stirring occasionally, until the flavors meld, about 10 minutes. Stir in the shredded turkey (or chicken); cover and cook until heated through, about 8 minutes.
Remove from the heat and discard the bay leaves. Serve the gumbo over hot cooked rice, if desired, and top with scallions.