Preheat the oven to 425 degrees and grease a 9 x 13 inch pan.
In a large skillet, heat the oil over medium heat. Add the onions and peppers and saute until just starting to soften, about 2 minutes. Push the veggies over to the side and add the ground beef, breaking it into chunks spread evenly across the pan. Cook, undisturbed, for a few minutes until the beef starts to brown. Break the beef into smaller pieces and continue to cook the beef and veggies together, stirring occasionally, until no pink remains. Season to taste with salt and pepper. Drain off any excess fat.
Add the brown sugar, mustard, ketchup, Worcestershire, and apple cider vinegar to the pan. Stir well to coat the beef. Cook for another 2-4 minutes, or until sugar is dissolved and the mixture is well combined.
Spread the mixture across the bottom of the pan. Top with all but about ¼ cup of the shredded cheese. Spread the tater tots in even rows across the top. Sprinkle the tots lightly with salt and the remaining cheese.
Bake for 30-35 minutes until the cheese is melted and tater tots are crisp and golden brown.