In a saucepan, combine hot sauce, 1 cup of butter, Cajun seasoning, and chicken stock. Heat over medium-low heat until the butter is melted, stirring to combine. Set aside to cool.
Using a meat injector, inject the cooled turkey injection mix into various parts of each turkey wing. Make sure to distribute the injection evenly. In a small bowl, mix together poultry seasoning, Cajun seasoning, garlic powder, onion powder, salt, and black pepper. Rub the seasoning mixture evenly over the injected turkey wings.
Heat a large, oven-safe dish over medium-high heat. Add a bit of oil to the dish and sear the injected and seasoned turkey wings on all sides until browned. Remove the wings and place them on a bed of chopped onions, sliced green bell peppers, and chopped garlic in the oven-safe dish.
In the same skillet used for searing, add 3 tablespoons of butter. Once the butter is melted, whisk in 2 tablespoons of all-purpose flour to create a roux. Stir continuously over medium heat until the roux turns golden brown.
Gradually whisk in the chicken stock, ensuring there are no lumps. Allow the mixture to thicken into a flavorful gravy. Adjust the seasoning if needed.
Pour the prepared gravy over the turkey wings in the oven-safe dish, ensuring they are well-coated.
Cover the dish and bake in a preheated oven at 350°F (175°C) for about 2 to 2.5 hours or until the turkey wings are tender.
Once the wings are tender and the flavors have melded, serve them over rice, mashed potatoes, or your preferred side.