Preheat the oven to 375°F, positioning the rack in the upper third for even baking.
In a large skillet, cook the ground beef over medium-high heat, crumbling it with a spoon as it browns, about 10 minutes. If using fattier beef, drain any excess grease, but for lean beef, it's optional.
Add the chopped onions and diced bell pepper to the skillet. Sauté for about 5 minutes, stirring occasionally, until the vegetables have softened.
Lower the heat to medium and stir in the ketchup, mustard, garlic powder, smoked paprika, Worcestershire sauce, vinegar, and beef broth. Combine everything well, letting the mixture cook for another 2-3 minutes. Be sure it doesn't dry out.
Transfer the beef mixture to a 9x13 casserole dish, spreading it evenly. If your skillet is oven-safe and large enough, you can skip transferring to a dish and keep it all in one pan.
Sprinkle half of the grated cheddar cheese over the meat layer, then arrange the frozen tater tots neatly on top. Bake the casserole uncovered for 45 minutes, allowing the tots to become golden and crisp.
Remove the dish from the oven and sprinkle the remaining cheddar cheese on top. Return it to the oven for another 5 minutes, or until the cheese melts beautifully. Serve hot, adding extra salt and pepper if desired.