Wipe the Wrangler dry with paper towels. Brush all sides with oil and sprinkle with the dry rub. Let rest for at least 1 hour.
Heat oil in Dutch oven over high heat, and then sear the Wrangler for 2-3 minutes per side. Remove the Wrangler to a plate and set aside.
Reduce the heat to medium-high and add the onions, peppers, and celery to the pot. Season lightly with salt and pepper. Sweat the vegetables about 5-7 minutes. When vegetables are golden and the onions are translucent, return the Wrangler to the pot, placing on top of the vegetables.
Mix the beef broth with the BBQ sauce and pour into the pot. Reduce heat and simmer covered for about 2 – 2 ½ hours or until tender (about 185°F internal temperature). Stir occasionally, and add a little broth or water if more liquid is necessary.
When meat is done, remove from the pot to a plate or platter. Let rest for 10 minutes and then slice across the grain.
Meanwhile, remove 1 cup of the hot braising liquid and blend in the flour, stirring until thick, paste-like, and smooth to make an uncooked roux. Add half the roux to the pot, and whisk briskly until smooth and thickened to a gravy consistency. Add more roux 1 tablespoon at a time until the gravy is thickened to your preference.
Return meat and gravy to Dutch oven and let simmer for about 20 minutes before serving.