Preheat your oven to 375°F (190°C). Pat the chicken wings completely dry with paper towels. In a large bowl, toss the wings with 2 tablespoons of vegetable oil, salt, pepper, garlic powder, thyme, paprika, and cayenne pepper until they are evenly coated.
Heat a large skillet or Dutch oven over medium-high heat. Add the seasoned wings in a single layer, being careful not to crowd the pan (work in batches if necessary). Sear for 3-5 minutes per side, until golden brown. Transfer the browned wings to a 9x13-inch baking dish.
Reduce the skillet heat to medium. Add the chopped onion and bell pepper. Cook for 5-7 minutes, stirring occasionally, until the vegetables are soft. Scrape up any browned bits from the bottom of the pan as they cook.
Transfer the cooked vegetables to the baking dish with the chicken wings.
Return the skillet to medium heat. Add the remaining 2 tablespoons of oil and the flour. Whisk constantly for about 1 minute to cook the flour and form a smooth paste (a roux).
Slowly pour in the chicken broth while whisking continuously to avoid lumps. Bring the gravy to a simmer and cook for 2-3 minutes, until it has slightly thickened. Taste and adjust seasoning with more salt or pepper if desired.
Pour the gravy evenly over the chicken and vegetables in the baking dish. Stir gently to make sure everything is coated.
Bake for 45 minutes, or until the chicken is tender and cooked through. The internal temperature of the chicken should read at least 165°F (74°C) on an instant-read thermometer. Let the dish rest for a few minutes before serving.