Poke each sweet potato a few times and microwave until fork-tender, about 10 minutes, rotating halfway through. Set aside and keep warm.
Meanwhile, put the carrots, garlic, tomato and onion in a food processor; add the vinegar, cumin, oregano, cayenne, 1 teaspoon salt and a few grinds of black pepper and pulse until coarsely chopped. Heat the oil in a large nonstick skillet over medium-high heat, add the vegetable mixture and cook, stirring constantly, until dry, 3 to 4 minutes. Add 1/4 cup water and cook, scraping up any brown bits with a wooden spoon, until the water evaporates, about 1 minute. Add the ground beef and cook, stirring and breaking it up into smaller chunks, until browned and cooked through, about 4 minutes. Remove from the heat.
Split the potatoes in half, scoop out some of the warm flesh and add it to the beef mixture; stir to combine. Divide the potato halves among 4 plates and generously fill each half with the beef-potato mixture. Top each with sour cream, Cheddar and scallions.
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