Crumble 1/2 pound of the beef into a saucepan over medium heat and cook for 5 minutes until browned and at least 160°F.
Add the yellow onion and garlic and cook for 3 minutes, then stir in the chili powder and cumin for 30 seconds.
Add the crushed tomatoes, broth, 1/2 teaspoon salt and 1/4 teaspoon pepper and simmer uncovered for 15 minutes until spoon-thick.
Shape the remaining beef into 4 patties and season with the remaining salt and pepper.
Cook the patties in a hot heavy skillet for 4 to 5 minutes per side without pressing until they reach 160°F.
Lay American cheese on each patty, cover for 30 seconds and toast the buns alongside them.
Place one patty in each bun and spoon 1/3 cup hot chili over it, then finish with chopped white onion.