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.
Brown the Wrangler over direct heat for 2-3 minutes per side. Remove to a plate to rest.
Heat oil in a Dutch oven (cast-iron is preferred) over direct heat 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 and move the pot to the indirect-heat side of the grill.
Mix the beef broth with the BBQ sauce and pour into the pot. 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 to the Dutch oven and let simmer for about 20 minutes before serving.
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