Place the ground beef in a large bowl. Add the peppers, chili powder, salt, and pepper. Mix with your hands just until seasonings are combined. Divide the mixture into 4 equal portions and form into round patties.
Add cooking oil to coat the bottom of a large frying pan. Heat over medium-high heat and place the hamburger patties in the pan. Cook the patties for a few minutes on each side until desired doneness. In the last few minutes of cooking, top the burgers with the cheese. Finish the burger with your favorite condiments and toppings. Serve and enjoy!