Preheat the oven to 375°F (190°C).
In a large skillet over medium heat, cook the ground beef until browned, breaking it apart with a spoon, about 5-7 minutes.
Add the chopped onion and green bell pepper to the skillet. Cook until softened, about 4 minutes.
Drain excess grease from the skillet.
Stir in ketchup, water, Worcestershire sauce, brown sugar, yellow mustard, garlic powder, onion powder, salt, and black pepper.
Simmer the mixture on low heat for 5 minutes, stirring occasionally, until thickened.
In a 9×13 inch baking dish, spread the ground beef sloppy joe mixture evenly.
Sprinkle 1 cup of shredded cheddar cheese over the beef mixture.
Arrange the frozen tater tots in a single layer on top of the cheese.
Bake uncovered in the preheated oven for 30 minutes, until the tater tots are golden and crispy.
Remove from oven and sprinkle the remaining 1 cup of shredded cheddar cheese evenly over the tater tots.
Return to the oven and bake for an additional 5-10 minutes, or until the cheese is melted and bubbly.
Let the casserole rest for 5 minutes before serving.