Add the vegetable oil to a heavy bottomed stock pot and heat it up over medium heat for about 1-2 minutes.
Now use a whisk to stir the oil while you gently sprinkle in the flour. Continue to stir to ensure there are no lumps.
Continue cooking the roux over medium-low heat, and stir constantly with a whisk or a wooden spoon, until the roux is the color of chocolate. This will take about 15-20 minutes to achieve.
Once the chocolate color is achieved, add in the andouille sausage to fry it up.
Fry the sausage for about 3-5 minutes, stirring constantly to ensure the roux does not burn.
Once the sausage begins to brown, add in the diced onions, bell peppers, and celery. Simmer the vegetables along with the sausage, until the vegetables begin to soften, about 2 minutes. Add in the minced garlic and stir it around with the veggies and sausage for about one minute.
Gently add the greens to the pot. They will initially overflow if the pot is not big enough. Use a large spoon to mix them in with the roux and sausage.The greens will cook down, and you can continue adding them.
Now Gently pour the water from the turkey wings into the pot with the roux and vegetables. Add additional water to just cover the greens.
Add the cajun seasoning and bay leaves into the pot and stir well to combine. Taste and adjust the seasoning by adding more salt and pepper to taste.
Cover the pot with a lid and simmer for 30 minutes.