Preheat oven to 450 degrees. Wash and dry all produce. Cut sweet potatoes into ½-inch-thick wedges. Toss on a baking sheet with a drizzle of oil, salt, and pepper. Roast until browned and tender, 20-25 minutes.
Meanwhile, halve and peel onion. Slice as thinly as possible until you have ¼ cup (½ cup for 4 servings); finely chop remaining onion. Peel and finely chop garlic. Halve lime; squeeze juice into a small bowl. Halve buns. Add 1 TBSP butter (2 TBSP for 4) to a separate small microwave-safe bowl; microwave until melted, 30 seconds. Brush onto cut sides of buns.
To bowl with lime juice, add sliced onion, ¼ tsp sugar (½ tsp for 4 servings), and a pinch of salt. Stir to combine; set aside to quick-pickle.
Heat a drizzle of oil in a large pan over medium-high heat. Add chopped onion and season with salt and pepper. Cook, stirring, until softened, 4-5 minutes. Add garlic and cook until fragrant, 30 seconds more. Add pork and season with salt and pepper. Cook, breaking up meat into pieces, until browned and cooked through, 4-6 minutes.
While pork cooks, in a third small bowl, combine BBQ sauce, pickling liquid from onion, 3 TBSP ketchup (6 TBSP for 4 servings), ½ tsp sugar (1 tsp for 4), and ¼ cup water (⅓ cup for 4). Once pork is cooked through, add BBQ sauce mixture to pan. Cook, stirring, until sauce is thickened, 2-3 minutes. Taste and season with salt and pepper.
Meanwhile, toast buns in oven or toaster oven until golden, 3-5 minutes. Divide toasted buns between plates and fill with as much BBQ pork as you’d like. Top with pickled onion and hot sauce. Serve with sweet potato wedges on the side.
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