Mince the round beef if needed. Chop the large onion and finely chop the small onion.
Heat a large pan over medium-high heat with enough oil to coat the bottom. Add the minced beef and chopped large onion, and cook for 5-7 minutes, stirring occasionally, until the beef is browned and cooked through.
Chop the tomatoes from the can and add them to the pan along with their liquid. Stir well.
Simmer for 5 minutes.
Add the red beans with their liquid from the can.
Stir in the chili powder, and season with salt and pepper to taste.
Simmer for 5 minutes more.
Sprinkle the finely chopped small onion and grated cheese over the chili, and serve.