Preheat the oven to 350°F.
Season the chicken wings with salt, black pepper, paprika, and garlic powder. Sprinkle with 2 teaspoons flour and toss until lightly coated.
Heat about ¼ cup vegetable oil in a Dutch oven or oven-safe skillet over medium-high heat.
Sear the wings on two sides until browned. Do not cook them through. Transfer the wings to a plate.
Add the diced onion and green bell pepper to the same pan. Cook until softened.
Add the 2 tablespoons flour, paprika, and garlic powder for the gravy. Stir into the vegetables and cook for about 5 minutes.
Pour in the chicken broth and bring the gravy to a simmer. Cook until slightly thickened. The gravy should still be somewhat thin at this stage.
Return the chicken wings to the gravy.
Cover the pan and bake at 350°F for 20 minutes.
Remove the pan from the oven and transfer the cooked wings to a plate.
For a thicker gravy, place the pan over the stove and simmer until it reaches your preferred consistency.
Remove the gravy from the heat. Whisk in the cold heavy cream, followed by the cold butter, until smooth and glossy.
Taste and adjust the salt and black pepper.
Return the chicken wings to the gravy and coat them well.
Allow the Smothered Chicken Wings to rest for about 10 minutes before serving.