In a large bowl, mix the beef, green onions, chili powder, cinnamon, and a pinch each of salt and pepper until well combined. Form the mixture into 4 patties.
Heat a large skillet over medium-high heat. Add the patties and cook, turning once, until well-browned and cooked through, about 5 minutes. Place each patty on the bottom of a hamburger bun and top with cheese.
In a small bowl, mix the tomato and ketchup. Spoon a dollop on each burger and garnish with green onions if desired.