For the mashed potatoes, add the potatoes, garlic, and 1½ teaspoons salt to a large pot and cover by two inches with cold water. Bring to a simmer over high heat, then reduce the heat to low to maintain a simmer. Cook, uncovered, until the potatoes are fork-tender, 10 to 15 minutes. Drain the potatoes and return them and the garlic cloves to the pot.
Meanwhile, preheat the oven to 375°F with a rack in the center.
Heat the oil in a large oven-safe skillet over medium-high heat (I used a 12-inch cast iron). Add the ground beef and cook, undisturbed, until browned on one side, about 4 minutes. Break the beef into small crumbles and continue to cook until no longer pink, about 3 more minutes. Sprinkle with ½ teaspoon salt. Transfer to a bowl.
If the pan is dry, add another drizzle of oil. Add the onion, bell pepper, carrots, and the remaining 1 teaspoon salt and cook over medium heat, stirring, until the veggies are softened, about 5 minutes. Add the garlic, chili powder, and tomato paste and cook for 1 minute, until fragrant and slightly darkened.
When the potatoes are cooked, mash them with a potato masher, then gently stir in the buttermilk starting with ¾ cup and adding more as necessary to reach a fluffy texture, and the remaining ½ teaspoon salt until smooth. Add additional salt to taste, if necessary (I added about another ½ teaspoon).
Return the beef to the skillet, along with the broth, ketchup, Worcestershire sauce, mustard, brown sugar, and vinegar. Stir well to combine and cook until the liquid is thickened, 3 to 4 minutes.
Turn off the heat. Dollop the potatoes on top of the beef mixture in the skillet, then spread them in an even layer to cover the top. Sprinkle with the cheese.
Bake for 10 to 15 minutes, until the cheese is melted and the edges are bubbling. For more browning on top, turn on the broiler for 2 to 3 minutes (watch carefully to avoid burning). Let the casserole rest for 5 minutes, then sprinkle with green onions and serve.
Notes
TO STORE: Store leftover sloppy joe casserole in an airtight container for up to 4 days.
TO REHEAT: Warm in a 350°F oven until heated through, or microwave individual portions.
TO FREEZE: Freeze leftovers in an airtight, freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.